air tag owner

What to do if you find an AirTag - Apple Support

It is up to the owner of the AirTag to provide the information when they have marked it as lost. It would be best to just leave the AirTag in a location that the owner can find it using the Find My app, but not in an obvious location that others would see it. The owner will be able to see its last location if there was another iPhone nearby when it is placed there.

The OP has already done that, since they claim it shows the serial number and no other information is given. The owner of the AirTag could provide more information if they choose to when marking it as lost. I would not recommend holding onto it until that happens and suggest leaving it in a discrete location to be found by the owner when they realize it is lost.

Thanks! FWIW. My aim was just to provide the OP with an Apple reference on what they should do in this case. It was meant to augment what you have already provided.