In Texas, AirBnb collects the state tax by default and submits a lump sum to Texas each quarter. When I use the Custom option I am now required to pay both state and city tax so yes, I enter both a state level and a city level tax in AirBnb and I now pay both Dallas and Texas. That means I had to register with both the State and City and obtain a Texas Tax ID in addition to the Dallas Tax ID.
Below is what my guest will pay. Click on 'Occupancy taxes and fees' and you see the guest is charged 'Hotel tax' and 'Lodging tax' as I have configured in my custom options. I use 'Hotel tax' for the 6% State level tax and 'Lodging tax' for the 7% City level tax. You can see the guest is correctly charged a total of 13% of the nightly rate + cleaning fee ($61 + $25 X .13 = $11.18)
Custom State ("Hotel tax") and Local ("Lodging tax")
Below is for another host in Dallas. Click on 'Occupancy taxes and fees' and you see they are using the default 'Hotel Occupancy Tax (Texas)' and the guest is only paying 6% ($64 + $25 X .06 = $5.34). That means AirBnb is collecting and paying the Texas tax but this host is responsible for paying the Dallas tax out of their own pocket.
It is more effort remembering to pay the City and State taxes but by passing the city tax on to the guest literally saves me a couple hundred dollars each month and is very much worth the effort.