If China can take out CSGs with pretty much no effective counter measures, will the US be willing to send carriers to support Taiwan during/after a Chinese invasion? It's all a game of brinkmanship - might be time for US/China to dig out the old Cold War doctrines on how to win a conventional war without winning so hard the other side feels the need to start slinging nukes.

I wouldn't expect an attack on a carrier group to necessarily lead to all out nuclear War. Seems more likely it would lead to a similar response, to a similarly sized and themed target, if only to save face and demonstrate that an equal response to such attacks will happen.

What's the US going to do? Attack Chinese cities? And then watch their own cities burn?

The US isn’t insane, it pretty much wrote the book on proportional response there is no way that they would escalate from an attack on a military target to glassing civilian population centers.

No US president would issue such an order and even if they would the chiefs of staff would almost most likely disobey it.