The Soviet Union constituted Ukraine in its modern-day borders as a constituent republic (Putin has referred to this as a mistake), thereby in a sense creating the country of Ukraine as we know it today.
Under the Russian empire Ukraine was completely subsumed with no independent existence at all and no recognition that Ukrainians even existed as distinct from Russians.
That's a misunderstanding. Allow me to explain what the issue at hand here is.
Basically the region we now call Ukraine is a mix of territories that were historically inhabited by a number of peoples including but not limited to Poles, Cossack, Russians and the people we today call Ukrainians. The later of which were split into several different polities which shared a language and broad culture but did not have a distinct national identity.
The Russian Empire, for the most part didn't really care about all that and they carved up their administrative divisions based off conquest and the occasional administrative reform. This lead to a lot of administrative units that were mixed ethnically and culturally. And this was more or less fine because this was the era before ethnic nationalism blossomed in the 19th century so people cared a lot more about their local power structure than about any concept of nation. It's the same situation you saw in all European empires of the time like Germany, Austria Hungary, Turkey and why you still have countries like Belgium today.
When the Soviet Union took over from the Russian Empire they also didn't give a dam about the peoples they were ruling. However, their takeover happened well into the era of nationalism. So they liked to pretend they did because fanning the flames of ethnic nationalism under the banner of "separate but equal under communism" was good propaganda. So they redrew the maps and created new administrative units named after which ever the majority culture in the region was.
The result of these new administrative units was that a lot of times new countries and even ethnic identities where created where there previously were none. Suddenly and over night everyone who spoke the Ukrainian language and shared their broad culture was a "ukrainian". Even if his ancestors just a few generations ago would not have recognized the term. The same thing happened in other socialist nations like for example Yugoslavia where the Kosovo Albanians and Macedonians also sprang up as cultures over night for the same reason.
Now, if you know anything about European history you know this sort of thing newer ever ends well. But it gets worse. Because whilst the Soviet administrative units (called Republics) were ostensibly independent states ruled and inhabited by their named dominant culture they were actually just administrative divisions whose borders were drawn in such a way to best suit federal objectives. This meant that in most cases the republics were just as mixed ethnically and culturally as their old Russian counterparts. And unlike what we would consider mixed in the west this wasn't an even blend across the entire territory either.
The Ukraine is a good example of this. The Crimea and Dombass regions are something like 90% Russian. The western part is something like 90% Ukrainian. And the south-east was majority Cossack until Uncle Joe had a word with them.
And this is the "mistake" Putin is talking about. Because in one fell swoop the Soviet Union not only created a bunch of new nationalistic identities which were inevitably bound to try and revolt for independence but they also ensured that when they did the territories they would claim as their own would contain regions of heavily concentrated ethnic minorities stuck in unfriendly territory.
And if you have any knowledge of European history you will know what this sort of thing inevitably leads to. Wars, wars, and nothing but wars. And not pretty ones either. But wars of ethnic cleansing and genocide,