They won't go to war. There will be much sabre rattling, lots of sanctions etc etc.
My wife is from the Republic of China (Taiwan) and grew up with bouts of sabre-rattling by the People's Republic of China. Because I've read of much more aggression from the latter in recent years, I pass on this apparent threat, but she isn't concerned, despite large family connections in Taiwan.
Taiwan was, until recently, 'protected;' by American promises; maybe that's still the case, but probably not so dependable as, say, 15 to 20 years ago. Mainland China is a different place with a different and seemingly permanent leader; the new, modern Mao.
However, Taiwanese business is embedded on the mainland and economic disruption for both countries would be difficult. Taiwanese are Han Chinese and speak Mandarin (unlike Hong Kong for the latter), The Kuomintang, remnants from C.K.S. (Cash My Cheque), has always pursued the policy of a united China, only in different ways to the mainland. It's the independence party (currently in power, I believe) that adds to the threat as seen from across the strait.
Taiwan is a prosperous, modern and very civilised country (but with appalling architecture), has an effective and well-equipped military, albeit no match for the CCP. It is the largest producer of silicon chips and has an excellent technical and industrial base and one of the most effective democracies and efficient governments; certainly compared to the U.K. anyway.
I've no doubt that Taiwan will be incorporated into China at some juncture but an invasion would almost equate to a civil war and probably trigger much wider conflagration. If this can be done peacefully, as has been the aim on both sides when the Kuomintang were governing, so much the better. However canny and powerful the Chinese leader is, he has enough economic problems in his own country at the mo'. Not sure what gains would be made for China anyway. His Belt and Road strategy appears to be unravelling somewhat, and he needs to maintain/improve world standing, which has slipped of late. The recent 'containment' plans by geographically well-placed countries creates a potential threat for China but they're just that; plans. North Korea could be a fly in the ointment too. w.r.t. China.