This answer might not be satisfactory, but the greek philosophers would span the entire spectrum of the different situations you describe. On one hand, they would be recognized as people you could invite to dinner parties to get interesting conversations (See Plato's "Symposium"). Others would operate in more "academic" surroundings, like in Plato's academy ( https://www.iep.utm.edu/academy/#H4). Lastly you would have the "rogue" philosophers like Diogenes, who probably is best know for insulting both Plato and Alexander the Great ( https://www.iep.utm.edu/diogsino/ ), that lived as an outsider to society. When it comes to roman philosophers, without having a detailed knowledge of the subject, they would be more integrated into the urban society as senators, orators and historians with a clearer function (See Seneca, Plutarch and Plinius).