Are these all old posts on social media? And he refuses to take them down or he claims you are still in a relationship right now?

It sounds like perhaps he said you were the love of his life when you were two together but he doesn’t bother removing it now (not using the specific site or just can’t care less). Him keeping old post there doesn’t necessarily mean he is making announcements to the world. He isn’t saying he loves you as those are old posts and everyone who wants to look will see it’s old by looking at dates. So who cares. Nosey people could look at the date and come to understanding that those are not current posts

Analyzing your ex after years of not being together doesn’t seem to help you to move on.