This is how it could be handled if agreeable to all:
1) Specify in the purchase contract how existing bookings with stays after the closing date will be handled, e.g. who will host or co-host, who will get the payments, how any payments to the seller will be transferred, if applicable.
2) The seller snoozes the listing to avoid future bookings, or blocks off dates after the scheduled closing
3) Upon closing, the buyer sets up and activates a new listing, blocking off all dates booked before closing. I would only set up the new listing after closing, because if the sale falls through, it would get really messy with new bookings.
4) The seller notifies the guests about any new arrangements, e.g. whether there is now a co-host, whether there is a change in guest communications, etc. Give the guests the option of rebooking with the new owner, if the arrangement can accommodate it. I believe Airbnb will help them do this without penalty to either host or guest. Alternatively, the guest can leave the booking as-is.
5) When all of the guests booked before closing have completed their stay, the seller deactivates the old listing. The payments are handled as indicated in the purchase contract in 1) above.
This obviously isn’t “hassle-free” as you requested, but it’s important to have clear-cut, written agreements in real estate transactions, and disclosure of changes to the booked guests.
I also recommend you not take legal advice from hosts on this forum. 🙂 Buy an hour or two of an attorney’s time to make sure you cover all the bases legally.