In my opinion, when he was younger, after Dick witnessed a little spat/fight between Bruce and Clark that resulted in them not talking for like a whole week, he noticed that Bruce got broodier without Superman to bounce ideas around with, and decided he would help them out in the only way he (a small teen) knows how.
So he buys one of those best friend half-heart charms (yk what I mean, like one side says "best" and the other says "friends" etc) and he gives one half to Bruce who's like omg.. to share.. and then he gives the other half to Clark who's similarly pleased to be sharing a best friend locket with Dick.
But THEN, at a JL meeting or whatever, Batman notices that Superman has half of the same type of locket he has, and Superman notices him noticing, which prompts him to proudly gloat that Robin shared it with him, because they're best friends. But Batman has already low-key clocked on so he just sighs and reveals that he hid his under his glove or something, and he's like, "yeah me too." At which point Superman gets it, too. And they're both like a little embarrassed because Dick (a child) wanted to repair them from their (adults) argument, and it's a little shameful that he felt the need to step in. And they both kind of want to keep the charms because they are actually technically from Dick, and they aren't exactly upset to have a little matching charm either, so long as the others don't find out because there's no way they won't get bullied about it. So they decide to both go and pick out some charms of their own to share with him, too.
Of course, they're just little trinkets, and they break and tarnish fairly fast - but you can find the remnants of them deep in drawers in the manor, shoved in the edges of boxes during house-moves, or maybe sitting somewhere, left in the pocket of an old, out-of-use batman suit, a remnant of the first kid in their lives.