"Catching Feelings", imo, usually implies that you're envisioning a future with this person.... marry her.. have kids.. mortgage... yearly vacations to Disneyland....white picket fences,..dog and cat.
Now I'm guessing you yourself are a gentleman, since she's allowed you to see her every week. Otherwise, if you weren't, or even if she found you a little too clingy to a neurotic level, she'd probably start ghosting you for her own protection. But if this has been going on for a year, then that could only mean she's found a steady stream of reliable and 'safe' income that she can shorten her network. If she can rely on 10 other 'nice guys' to see her once a week at (ie) $500 an hour, including extras... then she doesn't need to spread herself too thin, finding other clients to top up her demanded income.
Reading the rest of your post, you're going off attractiveness, and I'll assume her 'skills' too... but I'm not hearing anything from a personal level, beyond just 'intimacy'. Not hearing how you two see each other outside those professional boundaries, or go above and beyond with her, or she with you... she's just looking good and giving your great sex.
How much do you know of her personally? Has she opened up to you completely in any small way? Told you a tragic story, farming for sympathy...?
From my own second-hand experience, as in my brother dabbled with the trade and fell into this trap with someone he saw frequently. She might be all 'sugar and spice' but once the 'transactional' becomes 'personal' there's a good chance you're going to get sucked down her spiralling life that she's kept hidden under her professionalism. One step, you're having the best sex of your life with a goddess tier provider; next step, you're in the middle of a street-beef with her 'ex-boyfriend-pimp' who's shaking you down for money she owed from a drug debt...
Now I'm not saying "Cinderella/Pretty-Woman" scenarios don't happen, they probably can... but those odds are better used buying lottery tickets.