I'm not sure if this clip from the 1928 film 'The Cameraman' is a seawater public pool, but it possibly is. In the film, the pool was on the ocean. (But you know how far that goes.)
Clip possibly of a seawater public pool from 'The Cameraman' with Buster Keaton 1928 : D.D.Teoli Jr. A.C. : Free Download, Borrow, and Streaming : Internet Archive
DDTJRAC - WW2 Rationing Archive - Sylvia Schneider
Bathing parks / public pools were popular back in the day when many people lived in cold water flats with no bathrooms. They had a sink in the room and a communal toilet down the hall. For a good cleanup they would go to the bathing park / pool. It is too bad most of the old-timers are dead from that era. It would be great to get some stories from them on bathing parks.
A one room cold water flat.
Captain of Wall Street 90014 - Los Angeles, 1974
D.D.Teoli Jr.
On another topic...
'The Camerman' film DVD has a great specials section with a fantastic documentary on hand-cranked cameras of the silent era. A must see if you have an interest in vintage cine' cameras.
https://upload.wikimedia.org/wikipedia/commons/d/d3/The_cameraman_poster.jpg
https://en.wikipedia.org/wiki/The_Cameraman