We have a couple that would like to book our Airbnb from Jan 3- February 21, 2022. We already have a booking for January 13 through January 17th, 2022. So, would the couple want to book from January 3 through February 21, 2022 have to do 2 separate bookings?
Yes, they would have to go somewhere else for 4 nights. You could suggest a nearby motel or another Airbnb.
You could tell them that if the other guest cancels you will reserve those dates for them but otherwise they will have to check out early enough for you to prepare for the other guests.