@Nikko0, you can check yourself to see if AirBnB is collecting the tax.
Go to your Host Dashboard and select your "Calendar" page.
On the Calendar, select an unbooked day. On the right side of the page the details of the day will appear.
Scroll the right side info until you see the "What do guests pay?" link.
Click on the "What do guests pay?" link and you will be able to see the exact pricing a guest would see.
If that price information includes your local taxes, then AirBnB is collecting them for you.
If not, they AirBnB is not yet collecting them.
I looked at your listing and it seems that AirBnB is indeed collecting Occupancy Taxes for you.