Nobody is going to disclose & use anti-satellite technology over internet censorship. Hell, China isn't even aiming for bulletproof terrestrial censorship - they are happy with "good enough".
If war breaks out is the key. They'd rather keep their ability to destroy it under wraps until it becomes a matter of national security. Disclosing it or using it prematurely over a benign issue such as internet censorship would be stupid.
In the unlikely event that SpaceX tries to enter the Chinese market illegally, I wouldn't put it past China to swat one of Starlink's satellites using a conventional anti-satellite weapon (one of the sort they have already revealed), just to make a statement. But I think SpaceX won't do this anyway; they'll continue to comply with local/national laws during peacetime. It's not in their interest to stir the pot and cause diplomatic trouble.
But more to your point I agree; they won't try to destroy the constellation itself over something as petty as a few people using Starlink to circumvent their 'Great Firewall'. People sufficiently motivated to get around the firewall already can, without the need for Starlink. The CCP doesn't seem to care about it; the firewall doesn't need to be perfectly airtight to control the population, it only needs to be 'good enough'. And they wouldn't want to expose any new anti-satellite weapons they have, particularly soft-kill weapons that might be addressed after discovery with a software patch.
China has previously demonstrated anti-satellite weapons multiple times just to demonstrate they have them (and maybe make sure they work), I doubt they'd be that worried about the cost to demonstrate that they mean it and are willing to use them.
Russia has done the same demonstration last year [1]. And yet they have not destroyed starlink, even though SpaceX donated many dishes to Ukraine[2].
So there still seems to be some restraint around the concept of shooting down foreign satellites. I guess it's a "mutual assured destruction" type situation: once you shoot down a satellite, you'd better be prepared to lose your own.
