Courtesan, or from the Greek ages, Hetaerae, as well as the Japanese term Oiran, I would think is clearly more of an intermittent close companion, to guys of higher income or other influence, as contrasted to other definitions that get thrown around. There’s simply more involved than bedroom activities for this type of relationship, to the extent that history is rife with references to specific gals of this nature, whom have had significant impact on world history.
So does a “kept” friend also fall within the concept? That’s perhaps the question of current societal norms. If she supports him in his goals, probably so.
I have a couple favorite reverences for historical courtesans, but I’ll spare you a dissertation as I'm only on my second cup of coffee. That said, I’d like to thank the Mod from the great northern frozen wastelands of the Midwest, that uses a roman emperors name as a handle, for recently reminding me of the French poet Baudelaire, who references the Greek courtesan Phryne in his work, Lesbos, in his collection: Flowers of Evil, for which I dug into my library for an old translation, and am currently going through again, found under a stack that had fallen over