James Webb Space Telescope reveals that most galaxies rotate clockwise

Clockwise relative to what? Does the universe have an "upwards" direction?

Or is it just relative to all the other galaxies?

Clockwise relative to our viewpoint, while we would expect that we'd see an equal number rotating in either direction no matter which way we looked or where we were looking from.

How does that follow?

I imagine there was already a preferred spin of gases immediately after the big bang, just due to random chance, so why wouldn’t that be preserved more or less?

That's the thing, we don't know any reason for a preferred spin and assumed it would be equally distributed. So this is an interesting fact.

There doesn’t need to be a reason, just random chance from gasses shifting around is sufficient.

I think you are misunderstanding the point being made: The _only_ random chance that is part of current models is "quantum uncertainty at big bang time" and we can give upper bounds for the variations that can be explained from that. So what's really being said here is "We found a significantly larger discrepancy between Milkyway-corotating galaxies and Milkyway-counterrotating galaxies than can be explained by ~initialisation randomness"

That doesn’t make sense, they can’t be assumed to have behaved like ideal gasses, thus turbulence alone can cause significant uncertainties.

Let alone all other possibilities combined.

No it can't. Turbulence does not introduce net-angular momentum. It just (re)distributes it. And the scale on which that "mixing" can happen is limited (essentially the speed of sound is smaller than the expansion of the universe in the early universe). So on large enough scale, it (~any vector value) must be add up to ~zero (up to the initialisation uncertainties). Or one of our fundamental assumptions is wrong. And that's why this is so interesting

Can you link the proof for these claims?

I don’t see any obviously titled ones on Google Scholar, such as proving it’s impossible for turbulence to “introduce net angular momentum”.

I don't have anything more than Newton's third law for you and that its effects also hold in general relativity. The "far away parts of the universe are disconnected" is from my astrophysics courses back in university and the number of lectures to the cosmic microwave background, mostly coming from people discussing the Planck mission.

But.. no, I don't have a convenient citation for you. And at least for the "angular momentum is conserved thing", I'd be surprised if you'd find a google scholar paper, this is early GR