Essentially, a Pokémon whose better combat stat is ATK would use a Melee Attack akin to that of a Zombie, while Pokémon whose better combat stat is Special ATK use Ranged, like a Skeleton, only with the VFX for ranged attacks the color of the Typing (Normal = Gray, Fire = Red, Bug = Olive, Fairy = Bright Pink, etc).
Next, with some Typings having a low chance (maybe like 10-20% of the time) of inflicting some kind of Status Effects from Vanilla based on their type. Examples include Poison Types occasionally inflicting Poison and Nausea, Water Types inflict a status effect that causes Drowning, Ghost Types inflict Wither Damage, Rock Types inflict Slowness, Dark Types inflict Blindness, and so-on.
As for damage caused by such "attacks"...if possible, maybe have the damage caused be based on which Combat Stat they use for their Attack. An example for such an equation could be...
(Melee Damage = ATK / 10) - For example, an Aerodactyl with 135 ATK would cause 13.5 HP (or around 6.5 Hearts) of Damage in 1 Melee Attack
(Ranged Damage = S.ATK / 10) - For example, a Sceptile with 145 S.ATK would cause 14.5 (or around 7 Hearts) damage in 1 Ranged Attack
If you feel it more balanced, maybe have Ranged Attacks be weaker, like this, instead...
(Ranged Damage = S.ATK / 20) - For example, a Sceptile with 145 S.ATK would cause a little over 7 (or around 3.5 Hearts) damage in 1 Ranged Attack
As for how quickly they can attack, I'd base that off of their Speed, but idk a good number to divide Spd by, because "Atk Spd = Spd / 200" feels too fast, as the aforementioned Aerodactyl, with the base stat 150 Spd, would cause 20 hearts of damage in 4 seconds...
While allowing the Pokémon to use these attacks on players a la Legends: Arceus would provide a good excuse for doing it in general, I would also recommend allowing Pokémon to use these "Attacks" on Hostile Vanilla Mobs (Skeletons, Zombies, Endermen, etc) as well. For example, a person activates Vanilla Mobs on a Server, and gets cornered by Zombies; wouldn't it be cool to be able to send out your Greninja or Decidueye and fight your way to freedom together?
I hope this idea is worth considering, even if someone only makes it as a side-mod, as opposed to a main mod feature...