Ignoring the argument with your ex for a minute, what sort of relationship do you want with your son? A personal story:
My parents split when I was ten, and my mother had primary custody. My father wasn’t a horrible person in an objective sense, but he was very much a “my house, my rules” kind of person when we I was with him. Whether that was because he had a different set of values from my mom, was naturally an authoritative person, or was himself struggling from the divorce doesn’t really matter. What matters is that I was 10, 11, 12, 13 and was really struggling to adjust to my parents split, and had to operate under a different set of rules when I was in his house. It was like walking on eggshells at his house, because I’d always screw up while I was there, and then the visit would be ruined. Biologically speaking, kids at that age already have trouble with following rules, so having an extra set was frankly too much.
Anyway, it changed over time from me being excited to see my father to me dreading to see my father. And once I became an adult and didn’t have to see him, I saw him less and less, and then talked to him less and less, and then I stopped. I’m in my 40s now, I’ve neither talked to him or seen him in over a decade, and I don’t really have any regrets. The stuff above wasn’t the only reason, but it was a major part of the puzzle.
Anyway, I think you’re technically in your rights to make your son show you what’s on his phone when he’s with you, but I wouldn’t do it, at least not by forcing him. If you’re worried about some of the games he’s playing, ask him what his favorites are, download them onto your own phone, and see if you can play them together. That will give you something to bond over, and you can also judge from your own experience how potentially harmful or not the games are relative to how fun they are. If you’re worried he’s on the phone too much while he’s with you, try to do more things to keep him interested, but also set aside some time for him to use the phone. Maybe say something like “It’s hard not seeing you every day, so it’d would be nice if you’re on the phone a bit less this weekend. I’ll try to make sure to stay off mine as well.” But make a couple 30-minute blocks on the weekend when that’s what he’s doing if he wants. If you’re worried about social media, I understand, and he shouldn’t be on it at that age, but you’re not going to save him from it by forcing him to show you what’s there. It’s best just to try to make sure you have a good relationship so he feels comfortable telling you about anything there that you really should know about, so you can help him navigate it before he gets to the age where he’s just not going to tell you because he’s a full on teenager. Maybe you can sign up for his preferred social media and follow/friend him so you can, again, see what he’s seeing, but I wouldn’t force that one if he objects. But he’s 11 — if you show genuine interest, he’ll probably let you in. If you let him get the feeling that you don’t trust him and are spying on him, he won’t, and you should stop at the boundary he’s set rather than try to break through it.
The way you’ve described things sound so much like what my father would do in 2023. So again, it depends what relationship you want with him.