Not necessarily. If the PLAN is nuked in territorial waters that isn't recognised by the US, then China can choose to retaliate against the US mainland and its cities or choose to back down and not retaliate. The former means certain destruction, the latter means the entire Chinese mainland is free from nuclear war. If the US goes down the path of nuking the PLAN, escalation is not a sure thing. China may even be the first to nuke the USN because the calculus is true both ways. Nuclear escalation is no longer a simple binary, in fact it has never been. Only Russia says any nuke no matter how "tactical" in yield and placement is going to be retaliated in full. I think it's important for China to also officially declare this in order to discourage US tactical nukes being used on Chinese military targets far from the mainland.
China has publicly announced no such policy and neither has the US. China's nuclear policy actually makes it unclear whether it will retaliate or how it will retaliate if only military targets are nuked. There is a lot of nuance and complexity when it comes to nuclear escalation and exchange.
And Russia is obviously bluffing. They will not go for Complete Nuclear suicide if they think the war they are fighting will not lead to existential crisis for the Russian state and people. So, even tactical nuke attack will be swallowed if the objective was limited. But they will retaliate with their own tactical nuke on their opponent. So, the opponent will have to be ready to see huge casualties in their own ranks. China openly declaring so will not make it believable either.
In fact, I think US and Russia or any other country will even swallow losing one city and only retaliate proportionally instead of going for a national suicide, if they think the enemy will only attack that one city. All out nuclear attack on all cities sounds like a good plan to create deterrence. But anyone bold enough actually do an attack on another country will find that Human beings have a lot of tolerance in terms taking losses or swallowing their pride. Even the most fanatic soldiers do surrender instead of fighting suicidally until the end. Most death row inmates do walk to their deaths instead of trying strangle their guards suicidally. Its human nature to try to survive even one more day if possible.
I think people just have a lot of inherent fear of Nukes. But nukes are just like any other weapon. They are used for advancing your goals. War can happen between nuclear states without becoming an all out nuclear shootout over cities. That kind of event will never happen because no one will escalate things to that level. They will either fight conventional war, and if they think they are losing, they will go for a negotiated surrender. The other party will always show restraint and try to advance its limited objectives instead of fighting an existential war of annihilation.
Even a all out war can happen without becoming a nuclear exchange over cities. People are intelligent enough to limit fighting to certain boundaries.
The reason war doesn't happen is because its just too costly without much benefit these days. In the past, the main resource was agricultural land or mining resources. Now a days, you can buy anything you want in the global market. Controlling land and people is simply not as beneficial as before. People themselves are more educated and national identity also exists. Thus, they are more likely to resist domination by another country. Which makes controlling more land even costlier.
The biggest source of wealth now is industry and trade. Things that are easy to destroy in a war. So, people do not fight wars anymore. The only wars that happen are civil wars. War between states are always limited in nature in order to stop losses on the most important that matters, Money.