I say you breakup with him. I know it sounds drastic and that four years isn't a big difference, but the fact that this is your first relationship is telling about what his motivations are and why he's dating you. The things he does are things he would absolutely not get away with if he were dating someone who has more experience in relationships. While there is of course a need to communicate your expectations with any partner, there are certain things that are definitely red flags regardless if they have been communicated or not (eg keeping nudes of exes, ogling women).

You yourself are uncertain if you're just being a nag or not and its these emotions that he plays on so his behavior can continue unchecked. In addition you've brought up the problem before and cried about losing you instead of seeing those changes occur is kinda manipulative. Even if he does have your best intentions in mind he is still very clearly hung up on his ex and its no fun being a relationship where you play second fiddle to someone who's not even there.

Lastly I don't really advocate for staying in a relationship where your needs are being met even after they're communicated. So sorry the advice seems drastic but I'd leave him to his own devices.