Multiple users can access the web interface at microscope.local:5000 (or the other options depending what works in your network). I have tried it with two or three concurrent users, it will be interesting to know how it holds up with a whole class. Are you thinking a class of 12, 30 or 200+?. One possible issue for this use is that it can be a problem getting a Raspberry Pi joined to the network in managed networks like Universities. In that case you could use a local ad-hoc network from a phone hotspot (with data turned off or even an old phone with no SIM. Or you can set up the Pi to serve its own network as in this post. The students would then need to join that network instead of the normal wifi.
This would give every student access to control the microscope as well as to view. They would need to be sensible. In principle it should be very possible to have a version of the web app with only the view and no controls. Not quite in my skill set though.