Does catch rate in the underground scale with badge progression?

According to Dragonfly cave, there's a new variable in the catch rate formula for VIII generation:

For regular wild battles, this modifier has one purpose: if you have not yet completed the main storyline, then if your Pokémon's level is lower than the level of the wild Pokémon, this value will be 410/4096 (~0.1). Otherwise, this value is 1.

This is somehow confirmed on Reddit:

Carried over from Sword/Shield, if a wild Pokemon is higher level than the Pokemon you have out, the catch rate is really bad.

So yes, you are experiencing better catch rates because your current Pokemon levels are higher and you have completed main game.