I think it's a mistake to conflate Ukraine and Taiwan - the drivers are quite, quite different.
For China, re-unification with Taiwan is a matter of policy - and is in the public arena. Failure to re-unify the Greater Chinese Nation would be a failure of policy, and would represent a failure of the political leadership. Such failure would be intolerable.
For Russia, the desire is for a stable border. The current "frozen conflict" provides that stability for far, far less effort than would an invasion.