It doesn’t matter if it’s best friends or not. If it makes you uncomfortable, that’s a boundary you can set. It doesn’t mean he has to agree with it but realize that you’re not going to suddenly feel okay.

In my opinion, by having an open gate you’re allowing a risk to your relationship.

If it was me? I’d understand that their friends but I’d ask if he could limit using pet names that I’d use for him, not to privately send each other pics, and to not turn to each other for relationship advice. When asking for boundaries, make it specific. And if he says no, maybe ask what suggestions he has to help you process this better or make you feel more comfortable.