To configure your inbox, there is not much to do :)
Your account is synced with Airbnb thanks to the official connection, nothing to do, you'll see all the conversations appears in a couple of hours, and new conversation right away in your inbox!
If you are already connected to Booking.com with full synchronization, there should be nothing to do. The permission should have been added by default. If you see there are no conversations synced, you can ask Booking.com to check if the "Guest messages" permission has been added.
If you connect a new property, there is no choice but to sync the messages.