Hi @SAldricH-tech,
I apologize for my previous unclear response. I meant to clarify that the cards in the searched deck displayed in the log are sorted to avoid revealing card information in that deck.
Regarding the shuffle, the rules state:
Any time a deck is searched by a game step or card ability, that deck is shuffled after the game step or card ability completes its resolution.
Therefore, I believe the deck should be shuffled after a search, regardless of whether there are legal targets or not.
Thank you for your feedback, and please let me know if you have any further thoughts on this!