I don't buy this nonsense about Putin having ambitions beyond Right-Bank Ukraine. Putin didn't expect such resistance, and he understands now that Ukraine won't allow itself to become entirely Russian. Western Ukraine is not a match for Russia ideologically or historically, and since the war began, Central Ukraine has become much more radical in its stance toward everything Russian. He now realizes that Eastern Ukraine is the only area where Russia can be tolerated , if ceded to Russia.
And please -- anyone who talks about European ambitions is either naive or deliberately spreading propaganda.