My new boyfriend still misses his ex, what should I do?

Anonymous
I've recently started dating a guy who broke up with his previous girlfriend about 5-6 months ago. They ended on good terms, there weren't any fights; they broke up due to external factors. Since then neither of them have reached out to the other. He says it's bc it's too awkward. He still has a high opinion of her, says she is a great person, which I'm ok with. However, the few times we've run into her (they still have a lot of mutual friends), he gets visibly flustered while she seems pretty composed. And afterwards, he's always sad/mopey for an hour or so.

The other day he said he was in a bad mood all day bc it was her bday and he realized he wished he'd reached out to her more and could still be friends. I understand it's natural to miss a good friend but the fact that she was his first serious girlfriend and that he's so emotionally affected by the thought of her/seeing her seems like a red flag. He talks about wanting to reach out but it being "too weird", which I feel like translates to him being scared that she won't be responsive to it or reciprocate, which would hurt him. One could say that he "chose" me, but it feels more like I was only chosen bc he doesn't feel like he has a good chance with her anymore.

I haven't told him these feelings. But I did say that if he plans on reaching out to her I would rather he did it sooner and I could just keep my distance until he figures it out first. He ofc insisted he had no feelings left for her, only likes me, and doesn't really "need" to reach out. But then we saw her again the other day and he got all weird and mopey again.

Is how I am feeling purely from some kind of personal insecurity? Or do I have actual reasonable and logical concerns? I do not want to hurt him by leaving him over this. He's a nice guy, but even nice guys can lead girls on, maybe without realizing it. I don't want to be an idiot and willingly be a second option/rebound. What do you guys think I should do?
My new boyfriend still misses his ex, what should I do?
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