Hello there, @cheri_masters ...
Full disclosure...I've never had experience with GoGuardian, but doing a quick Google search, it looks like it's a tool that helps manage Chromebooks at school districts and content viewed on the internet...among other things.
It is my understanding that if you were to add a YouTube video to your Studio library and then embed that Studio video into a course, that video is still being played from the YouTube server. For clarification, are students at your school not allowed to access YouTube at all? Does your school block YouTube via your GoGuardian application? Again, I don't have any experience with this, but if YouTube is being blocked, then I would suspect that YouTube videos cannot be viewed/played via Studio?
The other question I would have for you is...what do you mean by "shared with students"? Is the Studio video being shared in a course via Studio embed? Or, are you providing the students with a public link to the video as described in this Guide: How do I get a public link or embed code for media... - Canvas Community. Or, yet another possibility...is the Studio video being shared via the method described in this Guide: How do I share media with a user in Canvas Studio? - Canvas Community.
I may be totally wrong on this, so I am happy to be corrected on any of this...if any other Community member has better information to share. I hope this will help in some way, however. Take care, stay safe, and be well.