> We largely don't even support our own past unprovoked invasions, much less invasions by rivals against stable and prosperous liberal democracies that we have long-standing friendly relationships with.

Of course you don't support invasions of your puppet nation that only exists because of your intervention. But let's flip this around. Suppose that there was a second American civil war, one side lost and retreated to California. PRC funds the losers, stations troops there, signs a treaty guaranteeing to defend their independence. Do you think the US would ever, in a million years, accept that? Even after 75 years, it's obvious the US is going to state that California still belongs to it, and would try to reclaim it whenever possible.

If you looked at this objectively, rather than from your perspective as the defender of the puppet state, it would be clear that PRC's claim is justified. All the more so because not only was the territory rightfully theirs, but now they have a hostile power from halfway across the world threatening to use it as a staging point against them.

Your American lesson, also, does not disbar any country from having any claim to any land. America is by far the most egregious actor in the world stage because it routinely does, in fact, invade lands that are halfway across the world. It can be true that invading a country on the other side of the planet is wrong, and that seeking to re-unify your partitioned country is not so wrong.

That said, I don't particularly expect it to ever come to war, anyways. I think it's much more realistic that PRC will exercise political influence and economic pressure to achieve re-unification rather than invasion.