My hope is someone who is familiar with architectural history is currently working on an answer about that particular floor but as far as I can tell, it was unique to the Beverly Hills High School. According to the school, the high school with the so-called Swim-Gym was built in 1939-1940 and was designed by Stiles O. Clement. I found a few sources that identified inventor Glen Cook as the designer of the floor, but he didn't leave a large footprint so I can't speak to other schools that benefited from his talents.

That said, you asked your question on Ask Historians, which means you're going to get more than just a yes/no. While that particular feature may have been unique, the thinking behind it wasn't. From the October 30, 1941 "News From the Boys in Training at Camp Shelby, Miss", Lewisburg Journal (Lewisburg, PA):

Our regiment has the use of the YMCA gym and the high school gym in Hattiesburg several nights each week. Thursday night, 120 members of the regiment enjoyed the practice and swim in the pools in both gyms. School and other officials have been quite generous in permitting the use of their gym facilities. We also have the use of the gym in the McClaron high school for basketball practice.

This particular quote jumped out at me as I was doing the research to answer your question as it speaks to two important things. First, pools in high schools gyms were/are fairly common and second, it shows how schools in rural and suburban communities were more than buildings to educate children; they served a visible testimony to a community's commitment to its children's cognitive and physical development and to the community as a whole.

To understand that history, we can look at the evolution of school construction. I've answered other questions about the history of school buildings so I'm going to pull a bit from those. The first wave of school construction in America was in the mid-1800s as the notion of "common" schools spread out from New England. "Common" (which basically meant "public") was the idea that all children (by which politicians and advocates meant non-disabled white boys, and their sisters) should sit by side and learn together. This meant adults had to consider what it meant for a group of children to be in the same building for an extended period of time. This first wave of construction mostly involved a shift from school happening inside churches or town halls to the construction of buildings explicitly set aside for small humans. Inside the building, it meant a shift away from hard, unmoving pews to desks with chairs. This also meant thinking about heating in the winter, sanitation, hygiene, safety, and social engineering about who was best suited to teach. The general consensus was that teaching was women's work and asking a young, unmarried woman to teach in an unsafe, dirty place was unacceptable - not if she were to keep her reputation intact. (More on that here.) This meant schools became cleaner, more like a parlor than an also-ran, dirty space.

The second wave of school construction started in the late 1800s as free, public high schools were established across the country. By then, the femiminzation of the profession was complete. The overwhelming majority of teachers were women (mostly non-disabled and white), the overwhelming majority of those in power making decisions about education were men (mostly non-disabled and white), and school was increasingly something children did in service to the public good. Whereas the earliest roots of public education focused on education for a child's spiritual well-being, the goals shifted as those in power saw an educated population as an essential aspect of democracy. While schools still maintained routines and content related to Protestantism, new routines connected to citizenship and patriotism emerged. As school increasingly became something all children did, the "look" of a school took on new meaning.

School slowly shifted from a building where children spent some of their time, to a place where members of a community encouraged, shaped, and educated their youth to be citizens. There are numerous reports of High School graduations in rural communities in the mid- and late-1800s where, even though only a handful of students graduated, the event was marked by large celebrations by everyone in the town. Thousands of people turned out for recitation events where children rattled off passages from American texts. It became a whole Thing with a capital T. The significance and prominence of education meant that as towns and villages built new schools, they were more likely to select locations that were aesthetically pleasing - a point of pride, as it were. Rather than building a new school in the middle of town, two schools might be built on either end of town, perhaps overlooking a bluff or on a particularly attractive patch of land. Given there was more space, they were more likely to build out, rather than up. To be sure, this wasn't a universal truth for all communities. I get into the history of school construction for Black children here. I like to think of the wave of school construction leading up to World War I akin to stars appearing in the night sky; just a myrid of temples to learning popping up around the country.

But then... then came the Depression, the Works Projects Administration (WPA) and the New Deal. (As an aside, this is when many districts passed laws banning the employment of married women. Unmarried women could teach but once they got married, they had to leave as district leaders wanted to protect jobs for married men.) By the 1930s, school architecture had become its own branch of the trade and architects designed large, open spaces with lots of natural light, multiple entries, curving staircases, and Grecian or Roman columns. The WPA kicked school construction into overtime and funded thousands of schools across the country, added auditoriums, murals, and gymnasiums to others, and helped establish the look of the modern sprawling suburban American school.

So, to summarize, the first wave was about creating school buildings everywhere they were enough children to fill the seats. The second wave was building schools that reflected a community's pride in public education. What happened at the Beverly Hills High School was an example of what happened around the country: communities wanted to build something that reflected their commitment to their community and their children. There is, to be sure, an entire history related to school segregation, the decision of Beverly Hills to separate from Los Angeles, redlining, and more... but that's likely more than you're wondering about.

Finally, it is worth noting there are distinct geographic differences in school design, especially between the coasts. Due to climate, west coast and Southern schools tend to be open, with classroom doors leading outside and design that takes advantage of air movement. East coast and mid-west schools are more likely to have internal hallways to make heating more efficient in the winter. And despite what some like to claim, schools are not built based on prisons or factories. In some cases, the architectural firms were the same as the number of firms who specialize in large scale projects was finite, but the design of schools has always been about attending to multiple goals: aesthetics, population, budget, safety, and comfort.