You can edit open street map (https://www.openstreetmap.org/) to add the trails you want, they should appear on certain Gaia layers that pull from open street map, but it might take a little bit.
Yes, download the GPX file then proceed to https://www.openstreetmap.org/traces where you can upload the trace (I think you need an account) then once its uploaded click "edit" now you can see the trace on the map and edit/create the relevant features. Its not automatic, you'll have to trace it with lines, etc or adjust existing stuff to get it right but it doesn't take that long. I've updated a bunch of trails this way.
All too often I forget to stop the recording when I reach the trail head and my track ends up a lot longer than expected. The opposite of your experience. To clean up the gpx data, I use GPS Track Editor. Export the tracks gpx file, edit in the Track Editor and then import it back to Gaia. Not sure if you can extend the Track.. but worth checking it out.
Public tracks are now available in the app. Please upgrade to version 2021.2 in the App Store (iOS) or version 2021.1 in the Play Store (Android) and you will be able to turn on Public Tracks in your Map Overlays just like on the website. In iOS, tap Layers > Map Overlay > toggle on Public Tracks. In Android, tap Layers > scroll down > toggle on Public Tracks.
Public tracks are now available in the app. Please upgrade to version 2021.2 in the App Store (iOS) or version 2021.1 in the Play Store (Android) and you will be able to turn on Public Tracks in your Map Overlays just like on the website. In iOS, tap Layers > Map Overlay > toggle on Public Tracks. In Android, tap Layers > scroll down > toggle on Public Tracks.