Also, a Pokémon in your party evolving only if you catch another specific Pokémon would be neat and unique!
We do kinda have that. Mantyke needs to level up with Remoraid in the party, and Accelgor / Escavalier need to be traded with each other.
In a broader sense I'd either try to keep away from the more quirky methods like "Flip the game system upside down", "Trade with this specific Pokémon (and they're version exclusives)" or "Take 49 HP damage then go to this place", or go balls to the walls with them.
Like, if we're going quirky, we're going quirky. Why not steal from Digimon and have "knockout X Pokémon of Y type" as an evolution requirement, or "be bred in captivity + have Pokemon of Z type as a father", or even have "faint in battle" as an evolution method into the Ghost type. Heck, I'd be down to go all the way to "dance around a stone during the full moon" with QTE.
Is it very weird and different from traditional Pokémon, yup? Could it be awesome and help set the tone of New Pokémon (since they're clearly trying to usher a new era of Pokémon games with different expectations here)? Also yup.
That said, I do love the status idea given, I think it could be super fun. I'd also suggest that hypothetical Grass Type to evolve into a carnivore plant if they end the battle under Infestation.