Yess, I can confirm it. Happens to me.

I think I have a variation on this where it NEVER appears :/

Have you checked whether your secondary drive is mounted beforehand? Is it mounted in the same exact place as last time (i.e. when you selected the path to your secondary game library)? I don't know how Cinnamon handles this but I recall some KDE users complaining about the external drives directories being somewhat randomized each time, leading to similar problems. GNOME always mounts drives in the same exact location, in case that's your issue.

Have you checked whether your secondary drive is mounted beforehand? Is it mounted in the same exact place as last time (i.e. when you selected the path to your secondary game library)? I don't know how Cinnamon handles this but I recall some KDE users complaining about the external drives directories being somewhat randomized each time, leading to similar problems. GNOME always mounts drives in the same exact location, in case that's your issue.

I'm not exactly sure how Cinnamon handles drive mounting, but the drive name is always the same, it's set to mount on startup and is mounted when I go to look for it, and the drives are in the same order from the selection UI (which isn't alphabetical order, I'm not sure how exactly they're arranged). I'll go ask on the Mint forums about this, though, and see if any of the people there know more than I do. Relevant post is linked here.

The problem wouldn't happen on the drive name, but I think your distro creates a different container folder with a random name each time it mounts a disk in "/run/media" (or wherever Mint mounts external disks in root). It doesn't matter if you've automated the mounting on start-up, they are still considered external disks... somewhat temporary. In theory, it shouldn't matter if the directory is different each time.

In practice, Steam goes to the directory you selected with the GUI and there's nothing there. But it's because your SSD is not in that directory anymore. Even if the contents of your drive are still intact.

I've established a workaround for this issue, but the workaround may be asking a little much of the average user, so I won't close the issue myself.

I think your distro creates a different container folder with a random name each time it mounts a disk in "/run/media"

I've learned enough to say that this isn't the case. Named and mounted partitions are located at /media/[username]/[partition name]. It looks like the Disks utility is mounting at /mnt/[uuid], identifying them with /dev/disk/[uuid].

My workaround:

Editing fstab to identify with UUID=[uuid], and mounting at /media/[username]/[partition name]. Asking users, even Linux users, to edit system files like that could be risky, which is why I said it might be asking a little much. I used the guide located here. I found the device name for the drive with blkid --label [label name], and then the UUID with blkid [device name].

Having this issue constantly with a new install of mint. Is there any word of a fix?

I solved my issue:
Try opening the Disks program, select the additional storage drive, click the cogs button, select 'Edit Mount Options...', and ensure 'User Session Default' is off, 'Mount at system startup' is on, and finally that 'Filesystem Type' is not set as 'auto'. I changed auto to ext4 and that's what fixed it for me; put whatever that drive's actual filesystem type is. I moved the files to another drive, and formatted that drive to ext4 beforehand, ext4 apparently works best with Linux

I spent a few hours looking for a solution and trying various things, and I finally found the above solution on a post from here: https://www.reddit.com/r/linux_gaming/comments/13igx4z/steam_forgets_libraries_on_secondary_drives_every/

Following the above comment, I completed the same steps with no positive result. I then attempted with the addition of changing the "Identify as" option to the first label option "/dev/sbd1" instead of the one with the UUID and that worked.