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I know the Changeling can shape-shift into people or even other daemons. But is this a trait that he just does or can all Heralds of Tzeentch do this? Can any others shape-shift?

If memory serves it is a trait of this deamon specifically, if we rule out possession.

It is stated in his character description from the first demon codex for 40k.

While there is no similar canon demon you can obviously create one at your leisure.

I can’t Remember its specific traits, but it could be more that it’s specifically unusual and worth noting down.

Demons of Tzeentch are often all change and not stable, so it’s possible that it’s a trait it possesses that’s notable and the way it’s been used.

Since it would be odd for Slaanesh daemons to not have at least limited shapeshifting abilities, but not use them the same way.

And with possession being much easier than manifesting, it may not even be worth it for 99% of daemons if they even have it.

GW also doesn’t use Daemons as much as you would expect, so they don’t get expanded lore wise much.
They are supposed to be infinite possibilities within their scope at least, so I do think it’s not unique.
But unique as far as classification and use for the Wargame as GW sees it.

Powerful Daemons can assume forms other than their own but in most of the background, Tzeentch Daemons tend to have the best shapeshifting abilities.

Kairos Fateweaver once turned itself into two humans to escape an Exterminatus after it had sowed chaos on a planet. Another Lord of Change also bargained with Fateweaver to assume its form to trick an Inquisitor into wasting their knowledge of Kairos's true name.

For the Changeling specifically, it seems that its abilities are a step up from normal shapeshifting to the point where it is almost impossible to tell the difference between it and the genuine article it is impersonating.

This might be more headcanon than canon, but I always got the impression that Slaaneshi daemons tended to use glamours/illussions rather than fully shape-shifting. This fits their preference for telepathic psychic effects and probably matches their fluff a bit better.

That is, they're described as abruptly changing appearances/dropping the illusion once they've lured victims in. Ceasing flexing their illussion muscles seems more likely than them having such high-tier physical transformation abilities that they overhaul their appearances in an instant.

That said, there's that story about a Slaaneshi daemon who impersonates an eldar well enough to charm an eldar woman and get her to unseal a webway gate so the daemons can swarm her craftworld, so the difference between an illusion and a physical transformation (when it comes to infiltration/deception) might be mostly academic.

If the kitsune's illusions are able to completely fool all your senses, then the illusion is basically a transformation/conjuration.