tbh I don’t think it matters, so wherever you feel like doing it. I just leave it where the distro or file manager defaults to: in Ubuntu-based distros that’s /media/$USER/mount-name. For mounts shared across users you could drop the $USER.

Since FHS doesn’t specify where “non-removable media” should go, I don’t think it makes sense to adopt this recommendation as /media should be removable, but rather, “in case the media IS removable, then mount it to /media/”.

If they are internal and permanent (read: unlikely to be removed on a daily basis), I’d just mount them based on their purpose and not them being separate HDDs physically. If they are meant for logs, mount them at /var/log. If they are meant for your movies, /home/user/data is more than fine. In general FHS describes the directory hierarchy, not which parts of it are mountpoints and which are physically on the same media. Technically you’re fine having each and every directory on a separate HDD.

I’m also mounting them into /home/user/data while I don’t think hard-coding the user name in the mountpoint is a good idea. Besides, it needs the assumption that I’m the only “human-user” of this computer.

I may also mount them at /opt/data, but I’m not sure if it’s a good idea

I’m coming more from a server perspective but, fundamentally, all HDDs are “temporary”. Eventually that data might be in a bigger/faster/functioning replacement - so it’s best to treat the drive as something which can always be replaced.

Continuing that, you might mount to /mnt and then symlink that where you really want it, say …/games. That layer of abstraction allows you to replace the drive without much effect on install. Also allows for expansion via something like mergerfs (*no idea if that’s a good idea for your use cases)

I originally had mine mounted on /, to make them easy to type. But that set one of my highly opinionated friends wretching, so I re-mounted them to /media// to placate him and symlinked them to my home directory instead.

It’s frustrating how often Linux systems, when approached with a “where is the canonical location for ?” question, have an answer ancient use cases practically no one has anymore, but no satisfying answer for extremely common use cases like permanently mounted backup drives, where to put web server hosted files, or even where to install applications that don’t come from package managers (/opt/? /usr/bin/? /home//.local/?).

If it’s just personal files and backups, there’s absolutely nothing wrong with what you’re doing.

If you had, say, active system config files there, it would make things… complicated to say the least.