If Dusknoir with the "Spectral Breach" Ability gets Knocked Out while Recycle Energy is attached to it, does the Recycle Energy go back to my hand or not?
No, Spectral Breach is still in effect when the cards are going to the discard pile, so the Recycle Energy would be discarded.
Source: TPCi Rules Team (2020-11-12)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH4_71
SWSH4_71
SM11_212
SM11_212