This is presuming that Biden would aid in Taiwan's defense in the first place. Given the Biden family's coziness with China, I think that would be a coin flip at best, but maybe whoever is pulling his strings would have different priorities.
Given US intervention and conventional weapons, I think China would be able to do a whole lot of damage to Taipei and other cities with rockets but ultimately not maintain naval or air superiority and make a beachhead on the main Taiwan island.
Given no US intervention, the question is a lot more interesting, as Taiwan has a well-funded military on its own but just might not be able to stand up to Beijing forever when it comes down to pure numbers. No US intervention might also limit Beijing's ability to go ham, though, since if Taiwan is undisputed Chinese territory since time immemorial, why is Beijing destroying it? It would probably be a much less popular war among even Chinese patriots if it couldn't be spun as a war against the imperialist Americans and so on, and you can bet Taiwanese nationalists would make sure videos and pictures of war casualties and damage made it over the Great Firewall.
So I don't expect the Taiwan question to be solved by a shooting war within my lifetime at least; I think one side or the other will eventually cave (I'd prefer it to be the CCP, of course, but who knows) and there will eventually be Germany-style reunification. That said I'm sure Taipei felt safer under Trump than under Biden.