Taiwan at least already has missiles with the range to hit Three Gorges.  Don't know about Japan or South Korea but it wouldn't be hard for them to build one if they wanted.  All three could build their own nukes if they wanted.

You don't really need a nuke to destroy it anyway; a good barrage of missiles on the ship locks and power station would knock it out of operation for a while, and direct hits on the dam could damage it to the point where the Chinese would be forced to release water downstream to avoid catastrophic floods.

A nuke would be more spectacular of course, and you'd only need one hit to do the job.  And since China would probably respond to any attack on Three Gorges with a nuke you might as well go big or go home.

Let's put this in the proper scale, three gorges is a gravity dam. It holds back so much water that it slightly altered the rotation and shape of the planet.  Which means the mass of concrete is also huge.

Yes we could wreck the locks no problem. But it's a big chunk of reinforced concrete, compromising it structurally isn't going to happen via missiles.    That'd be like splashing 9mm off AR500 plate.  Might scratch the paint.

A dedicated bunker buster munition might have a chance but they are big and heavy and like to fall out of B2s  

https://www.reuters.com/world/asia-pacific/skoreas-spy-agency-says-north-korea-could-test-new-icbm-coming-weeks-yonhap-2023-03-07/

It's wintertime KimChee is always spicier in the Winter.