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Yes, its seen as vocational training. Rather than teaching trig or how to apply it or what it means, you get how to display sine waves on a specific TI model.

I'm old enough that my vocational training in high school math classes was on the venerable yet new at that time TI-81. That vocational training was not terribly useful in university classes, the rot had not reached that high (at that time)

Mostly up to highschool and standardized exams. In college usually there was no constraints though many professors stated that we have to clear the memory before the exam. I used to have an HP48 for most of my college years.

You can likely use whichever you want during class, but at test time (APs, etc), there are only a few approved models.

For the most part, the primary concern is which calculators are used on exams, not during class.