Nothing personal, I don't hate Mundo or how he plays, but his kit just feels... off (then again he's supposed to be an insane purple hulk so... maybe it's spot on? XD). So here's a few ideas that everybody can look over, ordered by what "slot" they'd take up in his kit, starting with his passive, which SOUNDS good, but all too often doesn't really come into play unless you can really drag out an engagement.
Passive slot: Maybe instead of a less effective, no damage delay version of Garen's passive, we could try something like the grey healthbars some champions can build up now for healing? Maybe a grey bar that builds up as you pay health costs, that starts healing you a bit once you stop paying hp costs for a few seconds? Perhaps one that has a "build condition" like nasus' q, where you can do something like use certain abilities or kill mobs to build a grey bar that's permanent (healing would ofc need to be waaaaay slower than Tahm's or Pyke's grey bar mechanics though or he'd just be near-invincible lategame). Additionally there could be a stat builder version of his old passive here too, one where he gets a flat ammount of hp/s every time he fulfills the farming condition (like maybe pay x amount in hp costs, get x amount hp/5 regen until game ends?)
Q slot: Current one basically lets Mundo alternate between being a skill shot based ranged champion and actually auto attacking, maybe switch it to a ranged/melee toggle like Jayce, with more damage in melee and slow on the ranged modes? Could also try making the ranged mode have a health cost per shot and just giving melee attacks a slow, or putting an effect similar to his current E slot in there.
W slot: Current one feels like it's just there to proc magic resist from his E slot and pay hp to escape cc faster. Maybe make the aura damage a dot debuff like poison mechanics to emphasize the "burning" of Burning Agony?
E slot: I honestly don't really have any ideas for this slot, I like the ability as it is now because it makes him more dangerous as his hp gets lower, and that kind of fits in with his lore and general kit themes.
R slot: Current one makes Mundo crazy fast, while healing for huge amounts. When I play him it almost feels unfair to be able to switch from chasing to dodging skillshots back and forth, maybe swap the move speed for a slowing aura so he's not such a pain to hit during an R rush, but can still chase/escape a no cc chase effectively?
These Ideas are just me brainstorming here, so feel free to reach out with your own ideas for changes to make Mundo more Mundo-like!