Although a proctor is somebody who watches that candidates don't cheat in an exam, the common usage in relation to LMS is, a real person, who is physically in an exam hall and does this job (among other things) is an invigilator. The term proctor is somebody who undertakes this job remotely, with support of electronic means. The proctoring software is the electronic means. It goes way beyond the web cam of the candidate - a second camera, often the smartphone, is needed - even room surveillence cameras and microphones are involved. As you can imagine this is a demanding thing any a few suppliers dominate the market (or dominated in the post-Covid era.)
But you talk of classroom supervision. So it does not eliminate supervisors (invigilators). How does it function? What does is do more than say the default Moodle?