Hypothetically they could require that you use a device with an included monitor (laptop, tablet) and require that no HDMI cable is plugged it.

This won’t protect against somebody who is willing to open the device up and probe the embedded DisplayPort (or whatever standard) pins, but that’s probably beyond the ability or interest of most people.

I don’t like any of this; if I were asked to install some school spyware I would refuse. But it looks like the plan is for the schools to also allow the students to take the tests there. People should do that instead. Hopefully some parents will be super pedantic and require schools to provide accessible testing space and not use the “you can test at home” option as an out.