no, but they are cops

Teachers dont own the school but the principal might own it and if not the principal the superintendent. Teachers are workers!

not bourgeois but they are kinda like cops, obviously horrible under capitalism but probably a good/necessary thing under communism.

:

To add on to that, they even have significant amounts of capital! They get paid tons, relative to the proles allowances. They also use a lot of their money to buy school supplies, and the school supplies are used to do their job, which produces money. Teachers literally do M-C-M.

You've heard of time and teachers being bourgeois, now get ready for this:

space-time as a concept is bourgeois. Einstein was a cop.