Same here, I'm not comfortable with my partner having a deep loving / romantic relationship after her first outside relationship that ended in way too much drama for my taste. She on the other hand is not happy with super casual sex only. A FWB-style compromise that works well for us is meeting up every 1-2 weeks for cuddles, talking, and sex, but no flirting, extended chat sessions, phone calls, etc. outside of that / interfering with our daily lives.

Sure checking in every now and then and saying it was a nice evening is perfectly fine. Probably sounds more controlling on my side than it is really. It's just a compromise that works well for both of us. No idea (and not really interested in) what the technically correct label is.