On the way home from a trip in December, I dropped an AirTag in the pocket my 3-year-old's stroller and forgot to attach it securely before I gate checked the stroller.
I got the stroller back when we arrived but realized a day later that the AirTag slipped out. I could see it at the AirPort but an ~hour of time trying to recover it wasn't worth it.
I put it in Lost Mode mostly for kicks and when you place it in lost mode you can give people a way to contact you. I left my number.
I watched the AirTag go from my home airport to Scottsboro, Alabama and I knew the lost luggage store was there, so I was confused.
A week or so later I got a call from a service company that handles lost and found for Southwest Airlines. There were able to use an iDevice (presumably) to get my contact information since I had placed the AirTag in Lost Mode. They mailed it back to me for the cost of shipped. I assume if they don't find the owner it goes to the lost luggage store mentioned in the article.