What you are describing is "a regular." I agree with everything others have said on this. I'll add that another advantage of having a regular thing is it allows a continuation of exploration. Like, "next time I'd like to try ______" or "next time could you bring ______?"
Having a regular thing going with an escort is not unlike having a regular business relationship in other trades. Yes, you're friendly, and you sincerely enjoy seeing each other when business brings you together. Maybe it even drifts towards a friendship, but otherwise it's the "professional relationship" you mention. Just this week for my day job I had a Zoom with a vendor whose contract was up for renewal, and when we got on screen we were both truly pleased to see each other after nearly a year of only being in touch occasionally by email. Then there are the baristas, barbers, trainers, etc etc... people who we know well enough to be greeted by name, and while not friends in the conventional sense there is still a friendly relationship.
Of course it's in the interest of business to have regular clients, escorts included, so I'll say I'm biased! But I see the advantage to both parties. Most of my clients are regulars, and it's nice to just get a text that says "come on over" and we pick up where we left off last time.