you should have received a "booking is confirmed" statement by Airbnb. If not, then the booking is not completed.also check in your message thread with this guest: does it say "pending" or "accepted", or what? are the dates blocked on your calendar? if it remains unclear, call Airbnb asap. find the number for Croatia by googling them, numbers are not on the Airbnb site, but you find them by googling Airbnb support. Good luck!
Payment is only collected from the guest when booking is confirmed, not before. Guest and host should have a booking number, and guest Lso gets a billing statement. if they don't have it=booking is not complete or valid.