If my Lumineon V attacks with "Aqua Return" to take my last prize card, but Lumineon V is my only Pokemon in play, do I win because I took my last prize before shuffling Lumineon V into my deck or do I lose because Lumineon V get shuffled in before taking my last prize?

Everything has to resolve before you check for win conditions, and in this scenario both players have achieved one win condition; the game would then be resolved by either Sudden Death or a Tiebreaker Game. However, if the opponent also has no remaining Benched Pokemon then they would lose due to 2 win conditions vs. only 1!

Relevant cards

SWSH9_40