There are several issues to be addressed here, all of which seem to stem from lack of trust and communication.
If you had rock-solid confidence that your partner was respecting your boundaries, you would not have felt the impulse to snoop.
If he had rock-solid confidence that he could trust you with his most private "stuff" he would not need to protect his privacy.
If your trust in your relationship was stronger, you would have already talked all this out with him, and all the issues would likely already be resolved, or at least well on the way.
I can't offer any real advice on your situation. I can tell you how it is with me in my primary relationship, though. When it comes to my Fidelio, I am transparent as sunshine. Nothing withheld, even when it's uncomfortable. There is no part of my life he is not welcome in. ( There are, however, many parts of my life he has no interest in.) He values this special privilege and place in my life, and as a result deeply respects and staunchly protects my privacy. Similarly, he is more transparent with me than anyone else in his lifetime, and I respect and protect his privacy. (He is a combat veteran, retired USMC, and there are aspects of his military service he does not discuss. I can respect that.) So the snooping issue would be a complete non-starter for us.
Good luck to you all, however you choose to deal with these challenges.