None of the other shown ships had assignments similar to the one of the enterprise, though.
And yes, technically it’s not canon, however it was the show runners’ stated intention.
None of the other ships in Discovery were explorer vessels like "The Enterprise?" I find that hard to believe. If Disco had totally unique uniforms because IT was a special ship (experimental and all that), I could maybe buy it, but that wasn't the case.
If the Enterprise was a brand new ship that had just been launched and we were meant to assume its flashy new uniforms were the latest style, I could buy that, too. Also not the case.
apart from the admirals, which seemed to change uniforms every few weeks in early TNG. and the extras/many guests, who either kept using the old jumpsuits or later used uniforms that opened from the front (actually a retooling of the older jumpsuits). Or Picard, who dug a leather jacket. Or sisko, who used a gilet and for one episode even had troubles placing his communicator on the new FC uniform correctly.
Well, you can argue "real world" production considerations, which account for most of this, or we can discuss what the intent was meant from an in-universe perspective. Obviously TNG kept the old school jumpsuits in use for a while due to budget considerations before they didn't need them anymore. Obviously the evolving admiral uniforms were the producers and costume designers fine-tuning a look as they went along. Obviously Sisko having difficulty with his communicator were because the uniforms were rushed into production and they were still also fine tuning the fit. None of those examples are really relevant to what we're talking about. We no more need discuss those than we would need to invent a "weight gain" subroutine created by Dr. Soong to explain how Brent Spiner's real-world appearance obviously changed over time since the actor is not literally an android.
Picard choosing to wear a suede jacket is also not relevant since that was captains' prerogative (as was Kirk's swingin' green outfit in TOS.) Sisko wearing a vest was meant to just be a part of the FC uniform (Picard even sported the vest in First Contact, it's implied to be beneath the outer layer.)
my point? Just that yes, there is a lot of variety now, but the uniforms have never been THAT uniform even in the TNG/DS9 era, the most uniform of them all. And of course the era that started the “different assignment, different uniform” idea.
Different assignment, different uniform is acceptable, but I don't buy that different starships/different uniforms fall under that umbrella. I don't think Starfleet would say, "Oh, crappy Cerritos-style ships, you get these uniforms to denote your lesser status," even in LD, which is a light-hearted look at Trek not meant to be taken all that seriously.
I simply wish that there was a unified look. I get that LD didn't want to just use FC uniforms because they wanted to give the show its own identity (as was arguably the real-world reason for the DS9 change), but if that's the case, just put everyone in the LD uniform and declare unambiguously that "This is now the official uniform of the 2380s!" It's not like it costs you anymore to draw it that way.