I would not do a ceiling mounted camera, the angle of view is going to be so awkward to be looking down at the teacher from above. I think the camera needs to be closer to eye-level. Wall mount is fine I guess but I just hate fixing things permanently in the classroom like this because rooms are constantly being rearranged year to year. Plus if the setup is too rigid, it cannot flex to accommodate the needs (or just different styles) of teachers and then teachers end up going rogue and doing their own thing. I would not be surprised if you go to all the trouble of building this, and then have teachers recording classes on their personal cell phones because the setup either doesn't meet their needs, or is too complicated for them to use.
Personally this is what I would do:
That's it. The teacher positions the setup a few feet away from where they will teach. Portable, easy to use, versatile, reusable, non-proprietary, relatively inexpensive. And a familiar paradigm: the teacher can teach to the cart just as if it were a student standing in front of them. There is something to be said for the psychological familiarity, versus lecturing to an empty room with a camera on the ceiling.
Also there is no way I would roll out OBS to teachers. Teachers click buttons. They click a lot. They go 8 layers deep and click some more. In OBS there is a lot to click. They will break it and you will have to fix it. If you can get away with using a simpler piece of software then I definitely would. Either of the webcams above have a video recording software bundled with them. Or heck... Camera app built into Windows has about the right amount of buttons for a teacher.
Just my 2 cents.