A tiny bit of Googling gives https://www.rd.com/article/public-toilet-seat-u-shape/ gives:
> This is an open-front toilet seat, and thanks to the American Standard National Plumbing Code, it’s the go-to for most public restrooms. This code was created in 1955 and further cemented by the Uniform Plumbing Code in 1973 by the International Association of Plumbing and Mechanical Officials (IAPMO).
You can follow the links in the article I linked, or do a bit more Googling.
It's not a single uniform law, but a code that then got (and gets) adopted by lots of localities using different legal mechanisms. See https://en.wikipedia.org/wiki/Uniform_Plumbing_Code
Most "commercial toilets" are designed to be easy to clean and run off of "mains" pressure - commercial buildings have enough flow that they can flush directly without storing a buffer in a tank. And many commercial businesses have normal "home" toilets, at least around here.