No, that is not how it works. As others have said, there is no paperwork to file. If the booking was made via the Airbnb system, you hit book (if host uses instant booking) and the reservation is made. No paperwork to file. If the host doesn't use instant booking, you send them a booking request for the dates, they accept it and the reservation is made. No paperwork to file.
Who told you there was paperwork? The host?
As for transferring the booking, I think you misunderstand. What others are saying is that the host should have sent you an alteration request, changing the booking from one listing to another. The guest then just has to accept it and it's a done deal. No paperwork to file. There would also be no additional payment, unless the listing you are transferring to is more expensive, in which case, the alteration request would show you what the additional cost is BEFORE you accept/decline it.
Instead, it seems like you made separate bookings for the two listings and got charged twice. That was all totally unavoidable if the host had simply sent you an alteration request as outlined above.
The people who are responding to you here are experienced hosts who have managed their Airbnb bookings day in and day out for years. I don't know why you insist on tell them they don't know what they are talking about.
And this forum has nothing to do with customer support. It is a community forum for hosts and guests to discuss topics and reach out for advice. Your experiences with CS have nothing to do with the people responding to you, so stop blaming them.