Currently, I don’t have my HDD mounted at startup.
When I open it trough dolphin it’s being mounted it /run/media/…
I know how to mount drives, but I’m not realy sure if there is any default/classic directory for permanent HDD mounting (if I mount something temporary I do it in /mnt)
And about how.
Now. When I have a new drive and open it trough Dolphin I need to create a directory on it and change its ownership from root to jm (jm is my user)
/media came later then as auto-mount was more was widely used. Now it is in /run/media
If you need to mount other hard drives permanently then better create a folder on the root folder like /data and mount it there and put the folder to favorites or however you like it.
The lazy way is to have a label on your partition - my Toshiba has T4 (ext4) which I use as an extension to /home for media (Plex), pictures, music etc.
Initially I made a folder /mnt/T4 and then used gnome-disks to tell it to mount there at boot.
Systemd makes a mount and puts it on as boot - but it’s been fine for a couple of years so far, and it’s easy (if the disk fails) to replace that disk, give it the label, and mount that same location with a new device.
Later on you can set up a systemd mount which is more efficient - but basically the location can be anywhere (and I find /mnt/ to be pretty permanent). /run/media is more like a temporary mount on the fly location.