I'm very much aware "professional" is used as slang to mean someone who generally conducts themselves like an eloquent businessman.
However, slang is slang. Officially, the definition of a professional is whether you make money for work rendered. The slang usage of "professional" is incorrect.
The slang usage might get added to the dictionary and become correct some day, language evolves, but as far as I'm aware today is not yet that day.
> slang to mean someone who generally conducts themselves like an eloquent businessman.
That's not the definition in question here. This is:
> exhibiting a courteous, conscientious, and generally businesslike manner in the workplace
The way I used the words "behave professionally" is very common in American English. You could use this phrase to describe a student, a volunteer, or even a dog at a dog show.