The phrase “in a professional setting” is correct and can be used in written English. You could use it to describe a situation in which people are required to behave in a professional manner or are expected to adhere to certain standards of conduct.
A breach of conduct meaning is, in short, an act that violates terms set out in a policy pertaining to conduct. Importantly, that act does need to be intentional. Instead, anyone can be guilty of a breach of conduct if they mean to do so or not.