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I used to mount network attached storage in /mnt until I had problems accessing it from a Snap. In searching for a solution it was pointed out that snaps are correct in being sandboxed from these types of folders, and users like myself are making things difficult for ourselves by using those system folders.
They said the best practice would be to mount them in a folder in your home directory. I've switched to doing that and it works great.
/mnt is for anything and everything. /media doesn't even exist on Arch based distros and maybe others.
/mnt is not for everything, it is a temporary mount point. For fixed drives that are constantly mounted you should use another location (that could be anywhere in the filesystem tree).
IMO you should use LVM2 or one of the high level filesystems that have similar features, and then dynamically create partitions and mount them as needed. E.g. Suddenly need 50G for a new VM image? Make a partition and mount it where you need the space.
Mount them where you need. Not /mnt and not /media. Maybe /var or its subdirectory, or /srv, or /opt depending on what kind of data you want to store on that partition.