In general, an F visa is a student visa. You are considered a non-resident, and you are not allowed to work. You can receive income as a student (stipend, etc) and you file a non-resident tax return.
An H visa makes you eligible for work and you are considered a resident for tax purposes.
That means that for 2022, you are a dual-status alien. You need to calculate your taxes twice, once for your non-resident status and separately for your resident status. Turbotax does not prepare non-resident tax returns or dual-status returns, you would have to find another provider. (I don't remember if you actually file the two separate returns, or if you combine them somehow.)
https://www.irs.gov/individuals/international-taxpayers/taxation-of-dual-status-aliens
There are general rules for dual-status aliens at that IRS link but I don't know if the tax treaty modifies them.
Since your return is due in a few days, I think you should get an extension. This may take a while to figure out.
I agree @pk is the ultimate authority on tax treaties.
