This Atlas Obscura article mentions:
> the OSS commandos pioneered lightweight and compact rebreathers, such as the Lambertsen Amphibious Respiratory Unit (LARU)
https://en.wikipedia.org/wiki/Lambertsen_Amphibious_Respirat... says:
> The LARU is what the initials SCUBA (Self-Contained Underwater Breathing Apparatus) originally meant; Lambertsen changed his invention's name to SCUBA in 1952;[2] but later "SCUBA", gradually changing to "scuba", came to mean (first in the USA) any self-contained underwater breathing apparatus.
Looks like the Navy wasn't interested in the LARU, while the OSS was.
"Up Periscope" refers to both a rebreather (presumably LARU) and the open-circuit Aqua-Lung, which you can see at https://archive.org/details/upperiscope00whit/page/150/mode/... :
> He liked the Aqua-Lung immediately. He found that it was much easier to control his depth than with the rebreather and there was no taste in the air he breathed.
In any case, the story takes place in 1943 ("Other ships were rusting, burned-out hulks as a result of the Japanese sneak attack on that Sunday morning almost two years ago."), while 'The Aqua-Lung was invented in France during the winter of 1942–1943' (Wikipedia).
The patent, in German-occupied France, was issued "some weeks later in 1943", so it's nominally possible that the idea could have made it to the US by the time the story takes place. However, Wikipedia adds that Cousteau coined the name Aqua-Lung to sell to English-speaking markets, which would mean post-D-day at the earliest, not 1943.