Two different underwriting approaches exist and they don't produce the same loan.
The conservative one is what @halyard described. You value the property on long-term rent, because a 30-night-minimum ordinance can arrive and the property still rents to a tenant. That gives a lower loan amount and a much more durable one.
The other approach underwrites the actual short-term income. Lenders doing this typically want twelve months of platform statements plus bank deposits that match, and they'll haircut it, often looking at a trailing twelve months rather than a peak season annualized. Some will accept a market projection for a property with no operating history, and that's the weakest version of the file because the projection is produced by a tool with no obligation to be right. Terms and what any given lender will accept change constantly, so get the actual requirements in writing from the lender before you build a model around them.
On the documents: yes, this can appear. A loan on a property whose income depends on a permit can carry a representation that the permit is current and a covenant to maintain it, and sometimes a requirement to notify the lender of any regulatory action affecting the use. Whether that's enforceable in a particular situation depends on the loan documents and state law, so an attorney in that state should draft it.
The piece worth checking regardless of approach is insurance. A property being used for nightly stays under a standard landlord policy may have no coverage at all when a claim comes, and a lender holding a mortgage on an uninsured property is in a worse position than one holding a mortgage on a de-permitted one. Ask for the declarations page and confirm the policy names the short-term use.
