In Elder Scrolls lore, are there any Argonian settlements that are entirely underwater? I mean, they breathe water, so why not, right? Well, they might prefer to live in the air; and it's probably hard to talk underwater, if you're vocal chords are adapted to speaking in air (obviously, some critters talk underwater, like wales, so it's potentially possible, and you can do sign/body language, I suppose, instead of audio). In any case, just curious about it.

Most industry is difficult underwater, what with the whole "fire doesn't work so well" thing. That means no forges and much of alchemy/chemistry off limits, excepting purely biological ones (not that such a thing is outside the realm of possibility).

Meanwhile, underwater, oxygen levels become much more of a problem. The trophic levels of aquatic life are necessarily more shallow than surface life due to the limited quantities of oxygen in water. Whole cities would probably require constant gardening and ensuring that the water remains crystal clear to avoid overtaxing the oxygen supply. (Especially if you start to go into industrial use of underwater biological chemistry.)

TES is set in a universe where magic allows mages to breath in poisonousness realms of oblivion, anything is possible ( air bubbles for alchemy and whatnot )

To the OP none that I'm aware of.

You might be getting slightly too hung up on the word "city". It wouldn't necessarily be a huge, 10,000+ population settlement. Might be something small with a hundred or 200 hundred argonians. Might be they live their because they are outlaws, or perhaps they are a persecuted conclave, similar to the one that lived in that secluded cave in Morrowind (the one you had to enter at dawn or dusk as it was protected by the magic of Azura). If we ever get a TES game in Black Marsh, I'd really hope for such a thing. It just seems to be something which would happen, you know?

There probably wouldn't be any "industry" in the usual sense - however, there might be some special types of industry specifically suited to the environment - "farming" of certain types of aquatic life forms, or perhaps unique alchemical products which can only be produced in the environment (maybe there's an underwater "vent"/hotspring nearby which has unique magical properties necessary for creating a certain type of potion or poison, etc). Seems like there's all sort of possibilities to explore with such a thing, from a story standpoint, and it would make an awesome use of the breathe water spell, which I've always thought suffered from too few interesting reasons to stay underwater for extended periods. If you're going to have water breathing magic, give me a reason to go underwater and stay there for extended periods.