Abilities » Sonic Slip
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)
Abilities » Sonic Slip | Errata » Sonic Slip
The original intention of this [Sonic Slip] Ability was to provide protection only from the opponent's attacks, not from your own. The new text will say, "When you play this Pokemon from your hand to evolve 1 of your Pokemon during your turn, you may prevent all damage from and effects of attacks from your opponent's Pokemon done to this Pokemon until the end of your opponent's next turn."
Source: TPCi Announcements (2022-02-09) [https://www.pokemon.com/us/pokemon-news/errata-for-garchomp-in-pokemon-tcg-sword-shield-brilliant-stars/]; Brilliant Stars FAQ; TPCi Rules Team (2022-02-24)