It ultimately doesn’t actually matter because in many cases these things are convention and there is no real system-based effect. So while it would be especially weird if your distro installed packages into those directories, it ultimately doesn’t matter. Someone already linked the filesystem hirearchy. See how tiny the /media and /mnt sections are?
I put my fixed disks into subdirectories under /mnt and I mount my NAS shares (I keep it offline most of the time) in subdirectories in /media.
The answer to your question why is because I arbitrarily decided on that years ago. That’s basically all there is to it.
The answer to your file ownership problems I can’t answer, because I don’t have that happening. My files are mounted like so:
LABEL=BigHD /mnt/BigHD btrfs nosuid,nodev,nofail,noatime,x-gvfs-show,compress-force=zstd:1 0 0