I run them as having regressed to a land dwelling state and cannot breathe under water.  Though with webbed fingers and toes they would probably win a swimming race while have a disadvantage at a foot race. They are simply another fallen great race with vestiges of their former glory (for me anyway).  If you wanted some close enough to their former selves to breathe underwater then those on Atlantica may suffice.  I do use them as sages of Atlantean technology so to use the stuff you may need to find an Atlantean!!

That's one of the many things I like about the races in Hypeborea.  There are no rules-based differences.

Since I use the AS&SH rules in my own post-Atlantean setting (i.e., after the destruction of Atlantis by "something best left unnamed"), and due to starting the campaign using Stormbringer 5th edition: my Atlanteans are more like Melniboneans, though aligned with Law, not Chaos. And they do have racial differences (again, since I started the campaign using Stormbringer, where there are mechanical differences). In AS&SH terms they are slight characteristic bonuses and penalties (which balance out), reaction roll penalties with humans and a knack for discerning how to use ancient Atlantean contrivances.

By intent, this was left vague and open to interpretation for your own campaign. IMC, an Atlantean may have semi-aquatic traits (including limited water-breathing and superior swimming), but this comes at a price: semi-regular immersion in salt water, or the skin begins to dry and slough off rather painfully.

I don't prefer to state the reason "why" Atlanteans present with these traits, because I think this best left to you, my fellow refs. Devolution, evolution, curse, sorcery, extra-species breeding, a fungus from Ouranos? You decide.  

Brock Savage wrote:

In my campaign, the golden age of Atlantis was shattered by Kthulhu et al during the Cataclysm of Old Earth. This enmity between Kthulhu and the Atlanteans persisted on Hyperborea, with mind flayers, aboleths, and deep ones striving to enslave, devour, and pollute Atlanteans wherever they may be found.  The dreadful corruption of the Deep Ones was so thorough that pure-strain Atlanteans are almost non-existent, living in remote family enclaves and only rarely walking unannounced among common men. Although much diminished and their scientific knowledge lost, the race of Atlantis still produces wizards, warriors, and mariners of note.

This is a great take on the Atlantean race. I still have a few that are keepers of ancient knowledge.  If there is a viable piece of tech found there will probably be Atlanteans nearby keeping it that way.
 

The only game benefit I give Atlantians is that they're all strong swimmers; they never need to make CON checks no matter how long they've been in the water.  And they do have to get a weekly soaking in salt water, though a sponge bath from a bucket will suffice.

As a matter of role-playing, all Atlantians love long luxurious baths and will happily spend hours in the tub if circumstances permit.  In Swampgate there is only one genuine bathtub; it's in the Thieve's Guild safe house and they charge extortionately for the use of it.  The center of the Atlantian community in Khromarium is a Roman style bathhouse, with all the decadence and intrigue that implies.

I generally run them as having only the slight appearance, the body parts being mostly vestigial and more or less useless, but still noticeable.

Although in my version of Hyperborea, there are also rumors that the Atlanteans of old still exist somewhere deep beneath the sea in one form or another. Whether that is true or not has yet to be discovered.