Local External Storage not working?

Nope, for snap it is totally different.
All Apps are installed under you home in .snap, e.g. ~/.snap. Applications suppose to access regular user files, but I do not use it and could not help you exactly.
Wiki says your snap files under $SNAP_DATA ( /var/snap/nextcloud/current/ by default)

Removable media

Also note that the interface providing the ability to access removable media is not automatically connected upon install, so if you’d like to use external storage (or otherwise use a device in /media for data), you need to give the snap permission to access removable media by connecting that interface:

$ sudo snap connect nextcloud:removable-media
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