I've noticed the 'just friends to lovers' arc is everywhere with Sam and reader inserts. It's almost a given—starting as platonic buddies in the gym or on runs, building that easy banter, then one of them gets injured or has a nightmare and bam, feelings awaken. The 'established relationship' fics are less common but I seek them out because they skip the awkward pining and get right to the soft, domestic moments that I'm a total sucker for. Sam making breakfast for the reader after a tough mission, that kind of thing.
Another huge one is the reader being a non-powered S.H.I.E.L.D. agent or a therapist. It gives a logical reason for them to be in his orbit without being a superhero themselves, and lets the story explore his burdens from a grounded perspective. The 'patch-up after a fight' scene is practically a genre staple at this point—reader cleaning his wounds, him trying to downplay it, quiet conversations in the med bay.
There's also a surprising number of fics where the reader is from Louisiana or has a connection to it, mirroring his background. It's a sweet way to build intimacy through shared culture, mentions of food and family. The themes always circle back to patience, healing, and building something steady, which feels very true to his character. I just wish there were more that played with him as Captain America from the get-go, dealing with that public pressure together.