When you earn a Gym Badge in Pokémon Scarlet and Violet the defeated leader mentions it will be easier to catch Pokémon up to a certain level.
I know Gym Badges make higher level Pokémon obey you, but does "easier to catch" mean badges also improve your catch rate for high level Pokémon?
Screenshot from Nintendo Unity - Pokémon Scarlet & Violet - All Gym Leader Battles (4:19)