If I play Garchomp with the "Sonic Slip" Ability to evolve my Active Pokemon and then Garchomp moves to the Bench, does the effect from "Sonic Slip" get removed?
No. It is an effect from an Ability, not from an Attack, so moving to the Bench does not remove it.
Source: Brilliant Stars FAQ; TPCi Rules Team (2022-02-24)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH9_109
SWSH9_109