first of all in an American context the cleaning floors example would probably be laughed out of court as in no way being understood as Public safety, which would probably go with something like this
https://www.austintexas.gov/blog/what-public-safety>Legal scholars define public safety as “the protection of the general public,” and they reference groups like police officers and firefighters as Public Safety Officers. Many governments form their policies on this idea of protecting people’s physical welfare. They often focus on combating crime in an effort to help community members feel secure, and they hire for roles like law enforcement officers and medical emergency responders.
however I am getting the feeling you have never actually been involved in the writing of a law before
Defining public safety occupations would be pretty easy, although a lot of lawmakers in order to cut down on the misunderstandings might just go ahead and write a list of occupations that count as public safety if they did not want to let the courts decide. In a Napoleonic system I might expect the defining of public safety and it's meanings to take up a page or two of work, depending on how the makers wanted to define it (list of occupations affected, defining characteristics of occupations that would be affected)