Yeah, LitRPG is the strangest misnomer. When I first heard about it as a sub-genre of SF/F, apparently labelled such around 2013, it just struck me as a weird descriptor that Westerners put on throwaway paperbacks/ebooks that take place in an RPG world, which Japanese fiction has been doing for decades longer across literature, manga, and animation.
As to RPG mechanics for SARP like leveling up, we've kind of been moving away from that. A character's military rank is the closest we really get (especially since players can only create PCs ranked equal to the highest ranked earned through RP with anything higher being an NPC, which is just a re-use of the common practice of a new character getting the level of your previous dead character). Skills and abilities used to scale up roughly with rank. But we've kind of moved past that with our characters' skills being more amorphous and even not required to list at all anymore.
It'd be easy to reintroduce more leveling mechanics, though. My favorite tabletop RPG series is Legend of the Five Rings, a samurai game, and the older editions that I played had great ways to level up or track various aspects of one's character beyond their physical/mental/skill attributes. Like you'd have honor (personal morals that get solidified or degraded based on actions), glory (how well known you are), and status (how powerful you are), and sometimes points in a wealth advantage depending on the edition. So honor was akin to alignment but on a sliding scale, then glory and status while similar reflected different things—the rarely seen Emperor would have status 10 but a low glory score because he's sequestered away from the masses recognizing him, but a heroic clan Daimyo might have status 7 but glory 10 because everyone knows who they are. A wealth stat essentially tracks your SAoY prestige system rank. I think there was once a thread about that last one.
I think something like the above could work and be easily implemented via wiki struct, but it's also very gamified and could lead to people caring about the wrong things when it comes to RP. Not really a fan of surveys or voting for player perks on a site-wide scale because they ultimately wouldn't be indicative of who actually makes the RP better, but within plots it could work well.