Answers
How do you video call on a school computer?
Use a browser-based caller, because a school computer almost certainly forbids installing anything. Naven, Google Meet and Jitsi all run on a web page with nothing to download.
School devices are managed: the administrator controls which apps and extensions exist, and that list rarely includes a personal messenger. A web page is not an install, so the restriction does not apply.
The remaining obstacle is the network filter. Schools commonly block by domain, and a blocked domain stays blocked whatever it serves. There is no legitimate way around that and a tool that offered one would be a problem rather than a feature.
Camera and microphone permission is asked by the browser rather than by the site, and on some managed devices that permission is itself controlled by policy.