Seems to me that we'd have seen other contestants wearing left behind clothing before now for blindsided players. The only time I recall seeing other players wearing former contestant clothing is when someone gives it away before tribal. If nothing else, those left behind bags would have been seen while members were gathering food.
I suspect that the bag is retrieved while the camera crews are setting up for the after tribal interviews, and likely makes it back to the Ponderosa before the tribe makes it back from tribal.
I’m suspecting that you are probably right.
There is also a firm Survivor rule against theft of another’s property — though in the past I have seen contestants looking into another’s bag of stuff and finding their idol but not taking it — which is why some rehide their idol rather than keeping it in their bag.
I’m guessing that Garrett could not have willed his idol to Spencer after the vote since it would have had to be done while he was still alive in the game.
Anyway I’m guessing that Garrett wants it for posterity’s sake as he joins that small group of contestants blindsided with an idol in their possession.