My advice: Unfortunately, the moment may have passed. Though you didn’t reject them for anything they necessarily did (as you stated it had more to do with your own insecurities), they still had to take and process that rejection. It might’ve been hurtful or embarrassing for them, or they might’ve just shrugged it off and moved on. Either way, you reached out and gave them a fresh opportunity and they didn’t take it. This sounds more like an internal conflict for you than it does a missed connection. You’re falling down a rabbit hole of “what could’ve been,” and that’s probably not a healthy place to go. That’s prime territory for hurting your own feelings.
If you need to take a break from this person to help get them off your mind, maybe mute their social media. You don’t have to unfollow or block them, but muting may help get them “out of sight, out of mind” and that may lessen your temptation to check up on them and watch every story the second they post it.
As far as the mutual friend goes: don’t do it. If they can’t be trusted, don’t get them involved. That just creates a layer to the drama that nobody wants.
Be gentle with yourself because I know this hurts, but you can’t force it to happen. Maybe you will run into this person organically and there will be a chance to chat, but I think you need space from the situation. It sounds like it’s consuming you, and that’s not healthy or productive. Unfortunately, it happened, you made your moves, and there’s not much else to do but try and forge ahead. If something’s meant to happen, they can reach out to you. You were the last one to initiate conversation, so you’ve done your part. I’m sorry you’re hurting and I hope you find the clarity you need to move on from this!