Sure they want Putin gone. But Putin isn't Russia, for all that his ego says he is. That's why they think Putin gone will change things. The rest is ridiculous hyperbole that I'm not sure anyone of any import has even claimed. For that matter I'm skeptical anyone's even said some of it at all. Things like "Break up Russia" and "erase the Russian language" simply aren't things most people would even think of as options.
Russia still has outs. They just don't have easy outs that let them save face, much less make gains from this war of Putin's. For example, they haven't even tried bringing countries placing the sanctions to the negotiating table. Hell, as far as I know, they haven't even tried to get a cease fire during negotiations. The only one who "needs" to win this is Putin. That's because if he signs a treaty that'll end the war and lift the sanctions, he won't even need to step down as part of it. Russia will eat him alive for being so incompetent as to start a war he couldn't win.
To be pedantic, the post USSR Russia is younger than I am. It's barely 30 years old. Even if we add in the Soviet Union, it's barely 100 years old. And the Soviets did their damnedest to break with past cusotms, so I'm skeptical of how much real continuity there is with the Russian Empire. For that matter, several of the states of America were founded as colonies before the Tsardom was turned into the Russian Empire by Peter I, and those states have bearing even in the present day. So I would say there's not as much difference in length of history and of gravitas there as you seem to think.