If I use Dusknoir's "Special Transfer" Ability to move an Aurora Energy to another Pokemon, do I have to discard a card from my hand per Aurora Energy's text?
Special Transfer is "moving" the Special Energy to another Pokemon, not "attaching" it like you would from your hand. So since the Aurora Energy is already in play you do not have to discard a card from your hand in this situation.
Source: Brilliant Stars FAQ; TPCi Rules Team (2022-02-24)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH9_62
SWSH9_62
SWSH1_86
SWSH1_86