# $USER is an environment variable
# which contains the current username
# so you don't have to change it
sudo chown $USER:$USER /run/media/user/storage # or use a better mountpoint
However I suggest using a mountpoint in /media, rather than auto mounting via a file manager (if you’re already using fstab/systemd then don’t use /run). Read the links below for further information.
For a permanent mountpoint, I'd do this
sudo mkdir -p /media/storage
lsblk -f # Copy the UUID for the partition you want to mount
# Edit /etc/fstab and add the line below
# making sure to replace <uuid> with the UUID
UUID=<uuid> /media/storage ext4 defaults,relatime 0 2
# unmount the partition, if it's already mounted
sudo umount UUID=<uuid>
# Mount it using the fstab entry
sudo mount -a
# run lsblk to see if it worked
lsblk
# if it's not mounted
# then post any errors and the contents of fstab
# don't reboot without first commenting out the bad entry
# by placing a # at the beginning of the line
# a bad fstab entry will cause issues during boot
So start in /home/$USER then cd .. twice to /, then cd to /media which by default doesn’t exist. Why not just cd /media? It won’t work any better but it’s easier.
The OP has the drive mounted at /run/media/user/storage (presumably /run/media/$USER/storage) which can be seen by using a simple command such as lsblk -f (or reading their post ).