Hopefully I'm not conflating fics, but I'm pretty sure it happens like this:
Steve saves Peter from a fire during a fight, but Ben and May(?) died in the fire. He proceeds to visit Peter, as promised, and brings a PB&J to him. He's going to go into the system (foster) and Steve doesn't want that to happen and decides to adopt him. I'm pretty sure it ends up being Steve/Tony, Tony/Steve.
I'm usually good at finding fics through tags, but I'm having no luck with this right now. I'm quite sure it was on AO3. Any help would be appreciated!
Some specific scenes I remember (this got long so I'm putting it under a cut):
Steve brings burgers to "bribe" Tony so that he'll agree to Peter moving in more easily. The team then help and create a bedroom for Peter overnight before the CPS(?) agents arrive the next day.
Peter loves robots and the first time he gets to see Tony workshop he's amazed and plays with Dum-E (specifically coloring I think?) Upon Steve preparing to go down to the workshop with Peter, Steve thinks that Peter might actually think that Tony works in a store/shop because they all refer it to the "shop."
Tony is super hesitant about interacting with Peter etc. but one night Steve puts Peter in Tony's lap while he makes cocoa. Peter then is super interested in what Tony's working on (an armor) via his tablet and makes color selection suggestions (purple is in there somewhere.)
I'm pretty sure Tony actually watched them on the cameras at times, because he saw himself, a bit, in Peter and wanted to see what it would have been like if he'd had a loving father. Tony freaks out after Steve discovers the watching (probably before he explains it.)
Two people come to the tower from CPS (?) to see if they think it's a proper home, safe, and to address the possibility of adoption etc. Peter wants to "play" on the tablet with Tony and Steve explains that Tony is busy and that was actually him working, not a game. Peter starts throwing a tantrum and JARVIS alerts Tony that he might be needed. Tony comes up and helps out. I specifically think he tells Peter that asking nicely goes a long better and that he has experience with how throwing fits doesn't tend to work well.
I think, maybe it was this one, that Steve and Tony planned on keeping their relationship a bit quiet initially and tell Peter that they were having a sleepover basically because Tony was too tired to go back to his floor (Peter then asks if he can have a sleepover with Tony in his room?) Peter goes ahead to breakfast before them and tells the team they have a "sleepover" lmao.
I think there was a press conference and Happy was meant to be watching Peter backstage, but he got away from Happy. Peter runs out, trips, and smacks his head on a step? Tony rushes to help him.