It is doubtful that she is "nesting" since she is stealing things from your home and just dropping them outside.
Nesting is common behavior seen in pregnant females that are close to the time of whelping, where the female prepares a space to first whelp and then nurture her young.
Oh...your female was not neutered, she was spayed  We know that she is not preparing to give birth since she is spayed. So I think we can rule out nesting, as well.
I think some personal playtime and her own toys might be a good idea. I have seen dogs who were very attached to owners "steal" their items and place them in an area that they consider to be theirs. She might need more time from mommy  She also might be bored and need a nice toy. I like a Kong, filled with peanut butter and then frozen. Hours of entertainment! Good Luck!
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