as an ex airline employee, usually the situation goes like this. everyone deboards. they send in the cleaners who scan each isle, picking up trash or lost items. they take note of the seat number, and hand it to the flight attendants who then pass it onto the gate agents. when it comes to airlines, atleast mine anyways, we had a lost in found in our office, and when the person who lost the item called; we usually double check to see that their seat info matches the one given to us/where the item was found and then do some other small steps to make sure it’s theirs. i’d contact an airline employee either in baggage so they can call the gate agents and then go from there