How does Airbnb accomplish this? Why would my bank give them my new credit card number? Is new expiration date typical x years plus current expiration date?

AIrbnb's new payment terms https://www.airbnb.com/terms/payments_terms

Payment Method Information You authorize Airbnb Payments to store your Payment Method information and charge your Payment Method as outlined in these Payments Terms. If your Payment Method’s account number or expiration date changes (e.g. for credit cards or debit cards), we may acquire that information from our financial services partner and update your Payment Method on file in your Airbnb Account.