Good afternoon, @brloon ...
The term "media gallery" isn't something native to Canvas (as far as I know). It may be possible that your school has integrated another video service into their Canvas environment...such as Kaltura. Does the name Kaltura sound familiar to you at all? That's my assumption...for what it's worth.
The majority of your posting sounds like a request to enhance part of the mobile app experience. I'm not sure if you know about this, but there's a separate area here in the Community where you can make these types of suggestions:
Canvas Ideas and Themes - Instructure Community (canvaslms.com)
You'll want to read through the linked Guides under the heading "Ideas and Themes" located here:
Community - Instructure Community (canvaslms.com)
...so that you can get a better understanding of how ideas work.
I know this might not be the answer you were looking for, but I hope it helps to answer your question. Thanks!