If that were the case, Kiev would have fallen..and Russian wouldn’t need to be directly involved.
Nope, if we are talking about all the Ukraine, I think they are pro-Europe by a slight margin. It is not the case for the Southeast. They are majority pro-Russian for sure, even if most are too docile to resolutively express their affiliations and take arms. I guess Kiev attempts to reclaim this territory radicalized many of them. Anyway, their aspirations are certainly limited to their areas. None are planning to convert Lvov to their ways.