Did the listing expire? If so and the item is set to auto-renew status a fee will occur when it is relisted.
And it would be called "auto renew expired" on the fee description.
Auto renew sold, would only be for a listing that had a qty more than 1 and it auto renewed upon sale.
Perhaps the sale was reversed. See if you got the relisting fee returned.
Are you sure it said "auto-renew sold" or did it say "auto-renew expired listing" possibly?
You will need to contact Etsy directly for answers. Just a word of caution ... your shop may be in jeopardy of being reported & shutdown due to you reselling items that are not personally handmad by you, which is against Etsy Terms of Use. You also need to add EU compliant shop policies.
Sorry but I am LOL, literally, as I would never try to contact Etsy over 20 cents.
I would be like the OP and wonder why this happened and search around for something that might have sold, but contacting Etsy has gotten to the stage that for me it is actually funny.
Look on your finance page and see if there are other fees associated with this item like transaction fee and processing fee. IT seems if it "renew=sold" there would also be other charges for the "so called sale".