Levels stop meaning anything beyond an indicator of when you'll evolve and learn moves. Like
>>56405221 says, set them to (an invisible) 50 with the corresponding stats like in the Battle Tower so you don't curbstomp everything just by having a bigger number. However, EVs will still matter to keep in line with the idea that trained Pokémon are stronger than wild Pokémon. Early Trainers and classes will have low EVs and worse AI, later ones will be more optimized with custom movesets and use more held items.
You only get to use up to the same number of Pokémon as the opponent has, the battle transition makes your party screen slide in where you select your first Pokémon and you see the number of Poké Ball icons your opponent has, which also indicates the number of Pokémon you can send out at max. Your understanding of the Trainer class will serve your predictions, like sending out Fire or Flying types against Bug Catchers, while an endgame Bug Catcher might have specific counters to your counters. Ace Trainers will be harder to predict. And like in the Battle Tower and link battles, you can only use certain items, and you're on Set instead of Switch. Only Trainer battles will function this way, the overworld stuff plays out normally otherwise. Losing a battle will cause you to white out and lose money, fainting will still lower friendship.
Additionally, do what Gen IV did with items like the Poké Radar where you can find new Pokémon. However, make the other protagonist the professor's assistant who shows up to give you a choice of a new item that unlocks a new encounter method, but make them rewards for different thresholds of caught Pokémon. You choose the Poké Radar or the Radio and either unlocks 30 new Pokémon across the game. You can technically catch over 600 in one game with all methods, but you have to earn those methods one by one and your main story team will feel limited which can lead to better designed challenges.