Curate, connect, and discover
I have a soft spot for Peter Parker in Gotham fics, but how about Peter in Central City?
Post NWH Peter Parker ends up in the DC universe. He starts being spider-man there, makes connections and befriends other heroes. Eventually, Peter overhears someone mention how everyone forgot Wally existed because of speedforce shenanigans.
Naturally, Peter has a lot of emotions about his own situation and goes to the only other person he thinks will understand his predicament for advice (even if their situations were pretty different actually).
Peter kind of fails to properly explain himself and the alternate universe thing though. So Wally comes to the obvious conclusion that Peter is someone he knew, or at least heard of, before the spell. When Wally realizes all the issues Peter is having adjusting to life without a legal identity he offers to take him in.
(It would be fun to combine this with birdflash and 'Richard Parker and Dick Grayson are the same person' AUs.)
(I also think it would be funny if Peter said, "Dr. Strange did it." Like imagine Hugo Strange chilling in his cell when the bats pop in and demand answers he doesn't have lol.)