I can not access my second drive (HDD)

Is a device file, so you don’t chown/chmod it. You chown/chmod the mountpoint.

sudo chown $USER:$USER /run/media/caner/db5e4d93-0478-4aab-b34e-cea7b62ff3e7

/run is a temporary filesystem, it’s a place where software can put stuff without affecting the rest of the system. You should mount it elsewhere using fstab or systemd unit files.

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