This so called arms race is only in western minds. It would be stupid to not think about this possibility and its consequences of course but this is the most illogical option by China.
The best option would be to advance their own semiconductor tech beyond TSMC and make it irrelevant, which so far is the course of action they are taking (alas only because they are forced by US).
Expanding on why capturing Taiwan is stupid: TSMC already has fabs and people with knowhow outside Taiwan. The fab assets are not as strategicly valuable as their knowhow. Plus, even if you acquire the knowhow, there's the supply chain: ASML, others, ASML's supply chain.
I think US might force ASML and TSMC to move to US in the coming years even stronger but more than that this arms race isn't getting hot.