I have the same problem. Snaps are confined to only files within $HOME. I keep almost all data under /media/ and this caused snaps to be mostly unusable for me, at least unusable for productivity apps where I need to process data. Some apps though are self contained, e.g. Spotify, for example, works fine for me as a snap.
The limitation stems from a design problem, details at https://bugs.launchpad.net/ubuntu/+source/snapd/+bug/1643706.