Kiev has not been under local rule ever since it was destroyed by the Mongol Empire during the mid-13th C. In the mid-14th C., it was incorporated into the Lithuanian Empire (the Grand Duchy), which later merged with Poland (the Polish-Lithuanian Commonwealth). By the mid-17th C., it was won from them by the Russian Empire, where it stayed for centuries, right up through the Soviet era.
So, in the present context of the Russian invasion of Ukraine, it is more of a restoration of their historical territory, rather than taking over a polity with a long-standing history. That goes for the rest of Ukrainian territory, except for Lvov in the far west, which was only added to Russia in 1939, and was historically a part of the Polish kingdom / Polish-Lithuanian Commonwealth back to the mid-14th C., before getting taken by the Habsburg Empire in the late 18th C. when Poland was partitioned among the major empires.
This post is not a normative justification for any side in the war, but a descriptive analysis of the deep historical dynamics that have led to the current state of affairs. Crucially, this war cannot be analyzed as though it were the Soviet invasion of Afghanistan or the American invasion of Iraq, since neither of those were restoring long-held territory of the invaders, and the invaders saw the target population as a wholly different Other, whereas Russians view Ukrainians as brothers, having grown up together in the same place with the same history and subject to the same formative experiences.
What distinguishes the West from the East, in this context? It is not a snapshot of their traits right now, but rather their long-term historical roots, not just in some static genetic sense, but more so how they were shaped into a cohesive people or ethnos over the centuries.
Following Peter Turchin's popularization in War and Peace and War, the main force that binds a bunch of people together, to think of themselves as Us against Them, and to form a common defense and polity for the purpose of preserving Us against Them, is being encroached upon by an expanding empire -- especially if it is across a meta-ethnic frontier, where there are totally different languages, religions, subsistence modes, etc., on either side.
The nations and empires of "the West" all grew up in the wake of the collapse of the Roman Empire. In fact, they were brought into being by the encroachment of the expanding Romans out of the Italian peninsula. This was most powerful in northwestern Europe, namely today's France, beginning with the Merovingian period of the mid-late first millennium. They were not Mediterraneans by culture, did not speak Italic languages, were more nomadic / less sedentary, and practiced a different religion from Rome (although they were similar from having descended from a common Indo-European source).
Some modern members of the West owe their existence to a second-order effect of Roman expansion, i.e. the expansion of first-order cases like France. Most obviously, Britain, who were occupied by the Romans, but not for long, and not so intensely. British identity was instead forged by the expansion of France, especially during the Hundred Years War -- much longer, and much more intense of a pressure than Rome ever was to the British Isles.
None of the Slavic peoples were even around for the Roman Empire, let alone its collapse. Their migration period was the second half of the 1st millennium, long after Rome had bitten the dust. And their migrations took them far away from the old Roman borders, namely toward northeastern Europe, so they had minimal contact with the first-order effects of Rome like France, and could not become second-order effects of Roman expansion like Britain did.
Only some southern Slavs felt the second-order effects of Rome, namely from the expansion of the Byzantine Empire (a first-order effect of Roman expansion). And much as an expanding Britain arose due to an expanding France, an expanding Bulgarian Empire arose due to an expanding Byzantine Empire. Still, Slavic people on the whole do not share the deep historical forces that shaped the West.
Rather, the peoples of Eastern Europe were forged together by an entirely different group of expanding empires -- the Turko-Mongol nomads from the Central Asian steppes, whether they were Khazars, Mongols, Tatars, or whoever else. As far as Indo-European speaking farmers who adopted Christianity were concerned, all of those Turko-Mongol speaking nomadic pastoralists practicing Tengrism or Islam were equal to each other, and equally alien to Us. This forging of identity took place during a separate time period as well, from the late 1st millennium to the early 2nd millennium.
Those European nations that sprung up in the wake of the Romans, were not subject to these later pressures left by the Turko-Mongols. So there is little in common to the particular historical forces that birthed the Western nations, and those that birthed the Eastern nations.
There is a portion of the eastern Mediterranean that was subject to both Roman and Turko-Mongol pressures, especially Anatolia, which is why it has both Western and Eastern characteristics. But the Aegean region is not what we usually mean by "the East" when discussing Russia vs. Western Europe. And in the Balkans, the largely Slavic population there today was not there during Roman times, so they did not grow up on the Roman frontier, only on the Turko-Mongol frontier, which is why the Balkan Slavs are more solidly Eastern.
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Getting back to Ukraine, the first major polity in the region was the so-called Kievan Rus, known back then as simply the Rus, from whom both Belarus and Russia derive their names. From what I gather in a hotly contested theoretical debate, the early ruling elite were likely Germanic / Scandinavian foreigners who quickly adopted local Slavic culture.
However, none of the Germanic migrations have left a genetic signature in today's genepools around Europe, whether Spain, Italy, or Eastern Europe (no Visigothic, Langobard, or Varangian blood in those places).  Generally, the elites out-reproduced the commoners in the pre-Industrial age, so if the Germanics remained in the places where they migrated to, especially as a foreign ruling elite, they ought to have left a sizable genetic contribution to the present-day populations of those places. And yet they have not. So, either they inter-married with the local majority as quickly as they adopted their culture, or they simply went somewhere else after awhile, perhaps dying out sometime afterward.
In either case, the Germanic / Norse / Scandinavian influence on the Kievan Rus must have been fairly minimal. They culturally adapted to the local Slavs, and genetically mixed themselves in (as a small foreign minority, not affecting things much), or took a hike before too long.
But this whole business about the Norse migration into Balto-Slavic Eastern Europe is ignoring the ethnogenetic cultural factor that makes all these disparate peoples form into a cohesive Us -- namely, a wholly different Them encroaching on Our turf. In the case of the Rus, this was the Khazar Empire (Khaganate) from the east. Centuries later, the Rus were brought down by the expanding Mongol Empire. During that entire time, everyone in the territory of the Rus -- whether Germanic or Slavic or Baltic just a few centuries earlier -- suddenly, right here and right now, felt the pressure from expanding Turko-Mongol groups originating in Central Asia. Germanics and Balts and Slavs would have instantly put aside their minor differences, against the Turko-Mongol menace, to forge a new single collective identity -- the Rus.
The next empire to rule over Kiev, the Grand Duchy of Lithuania, arose on the frontier of the expanding Kievan Rus, and largely took its place. From their origin near the Baltic Sea, they were also being hounded at the time by their fellow Balts during the crusades to Christianize them -- Lithuanians were the last in Europe to adopt Christianity. But then the Rus were also Christians rather than pagans, and their Slavic language and other culture was more strange to Lithuanians than that of their fellow Balts, the Livonian crusaders. The Lithuanian Empire was no less subject to pressure from Turko-Mongol invaders than other Eastern empires, at that time mainly the Golden Horde (the northwestern section of the Mongol Empire), from whom they won control over Kiev in 1362.
The primary pressure that forced modern Russia into existence was also the Turko-Mongol invasions under various incarnations. As they were closer to the Turko-Mongol action than the Lithuanians were, the Russians developed a far more intense cohesion that has kept them as the leaders of the Eastern European sphere ever since. In fact, once the Turko-Mongols were taken care of, expanding Russia turned its attention to the Lithuanian Empire on its other, western border, not to mention the fleeting threat of an expanding Sweden during the 17th C. Russia's capital was moved north from Moscow to St. Petersburg for two centuries, reflecting this shift in regional priorities.
Eventually Russia conquered the lands of the former Grand Duchy and much of Poland from the Polish-Lithuanian Commonwealth, including today's nations of Belarus and Ukraine. This unfolded gradually over the second half of the second millennium (see here for maps and timelines).
Later threats came from the expanding Ottoman Empire to their south, centering around the northern shores of the Black Sea. The Ottomans were Mediterranean, Muslim, and Anatolian mixed with a Turkic-descended ruling elite -- very different from the Russians or other Eastern Europeans.
So, during its entire history of ethnogenesis, Russia has shared the same fate as the lands of today's Ukraine -- pressured by Turko-Mongol empires from the east, the Lithuanian empire to the west, and the Ottomans to the south. As far as Russian ethnogenesis is concerned, "Ukraine" is simply one part of Russia -- and a very central part, at that. It's not way up in the north where the Turko-Mongol and Ottoman pressures were weaker. Ukraine includes much of the steppe-forest transition lands where the Slavic farmers were right up against the Turko-Mongol nomads.
Imagining Russia without Ukraine is like imagining America without Texas and the Southwest, on the border not only with Mexico but with the Indians (Navajo, Comanche, Apache, etc.), who served as the main cause of American ethnogenesis. Not surprisingly both have a history of fiercely independent horse-riding frontiersmen -- the Cossacks and the Cowboys. Sure, some parts of America look down on Texas, just as some parts of Russia surely look down on Ukraine -- and yet, America isn't America without Texas, and Russia isn't Russia without Ukraine.
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To conclude, here is a helpful post from Turchin's blog, while the Donbass "separatists" ("join-Russia-ists") were staging their protests back in 2014. He links to other articles of his about why Russia is not Russia without Crimea, as seen by the place of Sevastopol among the Hero Cities of the Soviet Union. A city with such sacred significance is hard to let go of for Russia. He argued at the time that Russia would not waste resources annexing eastern Ukraine because there were no sacred cities there.
However, those Hero Cities also include Odessa and Kiev, in addition to the Crimean peninsula, drawing a boundary around much of Ukraine's territory. They include other cities conquered from the Lithuanian Empire, lying in today's Belarus and Ukraine and Russia, such as Smolensk, Minsk, and Brest (and of course, Kiev itself). And another that was central to Russian expansion in that direction, St. Petersburg.
These Hero Cities were chosen for their role during WWII, but you can see that the list is mostly a rationalization of the earlier expansion of the Russian Empire.
Thus, Ukrainian lands are sacredly central to Russian ethnogenesis not only because of their role in the Turko-Mongol struggle, but also against the Ottomans, and the Lithuanians. And just as Russia is incredibly close with Belarus, being in a state union since the post-Soviet 1990s, Ukraine will inevitably be incorporated into Russia as well. State union, annexation, puppet government, whatever other mechanism may enact it -- it will happen.
Russia is simply not Russia without the Ukrainian lands. You can like that fact, you can hate that fact, and whatever stems from that fact. But it's a fact, and there's no point in denying it or remaining ignorant about it, when our government is so centrally involved in trying to break Ukraine away from Russia and into the US-controlled NATO / EU empire.
 See the discussion and citation in this old post on the greater genetic similarity in Eastern Europe, due to the Slavic migrations having taken place most recently, and in lands that were sparsely settled before then. I postulated the greater genetic similarity as a second factor, after the cultural / ethnogenetic factor, for why Eastern Europe shows so little separatism compared to Western Europe.
That continues right through the present situation, which I noted in the Ukrainian context back then, since "separatists" in eastern Ukraine want to join Russia, rather than split off into their own little autonomous nation, a la Ireland declaring independence from Britain. This is more of a reconfiguration of polities, rather than fragmentation like you find in the West (e.g., where Basques, Catalans, and whoever else, all want their own separate nations after breaking from Spain).