If a new person comes online and their very first post heaps loads of praise on a particular eatery and encourages others to try it, I think it is legitimate to ask "do you work for, own, co-own, or supply this eatery?"

It’s not rude, it is a request for disclosure.

It would probably be rude to then also add any additional assertions, such as "I think you must own this place and it is not nice to self-promote", but asking for the disclosure without any additional comment is well within the boundaries of what is socially acceptable.

all of the above is purely IMHO