If Breloom gets sent to the Bench after using its "Spore Ball" attack, can it still use its "Powdery Uppercut" attack on the next turn?
Yes, because it is a game state check and not an attack effect.
Source: Brilliant Stars FAQ; TPCi Rules Team (2022-02-24)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH9_4
SWSH9_4