@Marguerete0 A few responses to different details in your message...
First, I don't think we, as hosts, will see, in our side of the transaction, the added amount that AirBnB tacks on to the guest's bill. We'll continue to just see what the guest pays minus our standard 3%. (There is a sneaky way to see the rest of the guest's side, as I'll describe at the end of this reply.)
Second, in Austin, you should be paying the city a straight 9% tax (covers the entire amount due the city), and not any add'l 2% sales tax or use tax premium. In other words, up until now, you should've been filing once per quarter with the city (for a flat 9%) and once per quarter with the state (for a flat 6%). If you live in Travis County but NOT within the Austin city limits, then I have no idea what your amounts should've been.
As far as how AirBnB will remit the 6% to the state, my reading of what AirBnB sent us is that they'll be charging the guest an added 6% and passing it, in our name, to the state.
Interestingly now, if you set up a Special Offer to a guest (whether or not you actually submit it), you can see that AirBnB is tacking on that 6% even though they don't break it out (to the host's view) as a tax charge. How can you tell that? Well, when you made a special offer in the past, the amount AirBnB charged the guest over the total of your offer was about 12% Now it's about 18%.