"What will China actually gain from this? Not much besides scoring some political gains at home which they don't need anyway."
China views Taiwan as inexorably part of their homeland. The existence of a 'separate Taiwan' is kind of like a permanent stain to them.
Imagine if during major American political upheaval, Texas became it's own state again, and after takeover by Central/South American political entities, decided not to rejoin the rest of the US as the political situation stabilized.
Americans wouldn't rest until they reclaimed it.
I'm not justifying it and personally I would have liked to have seen a 'Chinese Federation' i.e. Hong Kong, Taiwan, mainland China, possibly even Manchuria as separate entities, possibly with 'Tibet' as managed-but-autonomous region. Instead of a single autocracy.