You can do this with the Flatpak version of Steam, but you have to give it access to the disks.
Flatseal is the easiest way to do this.
Open Flatseal
select Steam
scroll down to the "Filesystem" section
click on the + icon on the "Other files" area
either put in the full path, or use something like "/run/media" to give it access to all user-mounted storage devices (this value may vary depending on how the disk is mounted)
Restart Steam (if it was running). You should be able to access additional devices.