My partner and I went through some of that. We go to the gym together but don't work out together except to spot for each other mostly on chest day. But even then it is only on bench/bar lifts, not dumbbell or fly work. And aren't usually even working the same stuff the same day. But we do keep track of each other and spot when asked. And we try to finish together. If one finishes first, the other just gets on a bike or treadmill until the other is done and we shower and dress together so it isn't like we're not there together or in touch with the other but we rarely speak in the gym because I like to concentrate and time my intervals. When we started this pattern, my guy got his feelings hurt a bit that I didn't want to do it all together but he got over it and now takes his workout more seriously than he did and is fine with it. Just explain the rationale of your thinking. He'll get it if you talk about it.
As to food, I cook 95% of the time for dinner and we don't try to coordinate lunch. So dinner is healthy and sometimes I cheat at lunch and he doesn't or vice/versa. Breakfast we don't coordinate at all. Right now I'm good with my weight range (15% body fat at my age is lean) but he wants to lose 5-10 lbs so he's on a more strict breakfast/lunch than I am. Sometimes it is the other way around.
You can work through these issues. We have and consider our joint health something we do together. It bonds us even further.
Sounds like a good relationship. I've been less fortunate with most of mine regarding exercise. Cooking is a happier story.
One BF was a gym rat. And when I tried to join him he mocked me. Even though I was still in pretty good shape, although not the muscle guy he was. But then he was 11 years younger than me.
And it infuriated him when people thought we were the same age, or him even older. No one ever guessed I was the much older one. I think jealousy was driving his attitude.
Another BF was also into gyms. We went together, as a convenience. But once there we did our own thing, hardly saw each other in a large place. Afterwards back in the locker room was nicer. In the gang shower together, and the sauna.
My present partner doesn't do gyms. i think it's good when you can be there together. Even if doing separate things. I envy you.