They have (estimated) 1/10 the nuclear stockpile and limited delivery vehicles, it's mostly credible as second strike. That said, the launch hardware and command structure is mixed with the conventional rocket force so any conventional attack on Chinese rocketry is indistinguishable from first strike since no one can be certain whether attack is on conventional or nuclear assets. This ambiguity is by design. Doubt is when China moves towards nuclear parity.

About as seriously as anything in geopolitics - i.e. not at all, unless enforced by a credible threat from other countries. But it's a nice, zero-cost gesture.

It's a nice, zero-cost gesture US is unwilling to make.