You pay it. It's insane.
In the same boat here.
We actually got audited because of this. If you are an HST registrant, and have an HST number, your are NOT ALLOWED to have anyone else collect your HST oh your behalf - heard this directly from the CRA. If you are HST registered, then it is YOUR JOB to collect and remit HST.
But in order to prove that you have collected and remitted HST, you need to produce invoices that shows you have done so. Currently the guest invoices have no HST line item and no ability to add it. Oh but conveniently they added an occupancy tax line for 2023, which is 13% of THEIR guest service fee. So they are being complaint with CAD/Ontario tax law, but not giving hosts the ability to do the same.
The net result is no matter how much you up your price to try and include HST, without an invoice that says you have done so, the government will demand 13% on whatever your gross earnings are.
Was on the phone w Airbnb for an hour, all they said is that "they are working on it". Insanity.