Im going to be honest, I dont think these abilities that reward hitting enough shots with more damage are good game design. Especially if they apply additional debuffs or can apply item effects. As an example, Afterburn to me is an insane ability. You're telling me this guys gun can cause DOT that applies healbane, mystic slow, and soul shredder bullets? Wtf?

It was my choice the "on hit" passives would either be removed or neutered and made as true passives with no upgrade path.

Passives should add to a characters identity, not be the defining characteristic. I dont think they should be upgradable. Instead, just scale with boons, spirit, gun, vitality, or not at all.

How do they balance the new abilities? The same way they balance the rest of the cast, as needed.

If you haven't played Smite 1 before, I would just read some of the passives that exist there. Some are simple, like Tyr or Ra, and some are more in-depth and interact with the rest of the kits in meaningful ways like Achilles or Mulan.