That's a good question to think about actually. I don't think they handled it the way Russia is handling it now (assuming that this is in fact what's happening with Russia).
Actually the big European powers gave up their empires fairly quietly. Yes they sometimes fought wars to keep them on a case by case basis, but I don't think any of them launched large scale campaigns of invasion as a response.
I am sorry but Ireland, Kenya, the Malayan emergency, the Indian mutiny, the Vietnam war, Portugal’s wars, Algeria, Suez, Spain from 1820s+…
I would not call any of that quiet. And Suez was definitely an invasion.
Hell, US hegemony was challenged by Al-Qaeda and they invaded Iraq.
Russia is different in that rather than being a seaborne empire they were a land based empire. The Austro-Hungarians invaded Serbia when their Balkan ambitions were looking like being thwarted.
There were also significantly counter-culture movements against anti-imperialism similar to the russian anti-woke-culture war (after all it discredits imperialism) and thus dissolves the russian empire if looked at through this lense. They were just discredited after hitler dialed imperialism up to eleven.
Actually the big European powers gave up their empires fairly quietly. Yes they sometimes fought wars to keep them on a case by case basis, but I don't think any of them launched large scale campaigns of invasion as a response.