I had a very similar setup at one point, and what I did was just install Linux on the SSD. I'd recommend against mounting the HDD as /home
as it'll make your file manager feel sluggish, and would be an overall bad experience.
I used to just symlink directories from the HDD as ~/Pictures
, ~/Music
etc. and most software would just be able to work with those. You don't really need to move software to your HDD since they rarely take much space, and moving to HDD will make them very slow.
For games, Steam and Lutris will let you select the installation directory on a per-item basis so you should be just fine.
That said, maybe you could use this opportunity to get a new larger SSD and then you won't have to worry about this anymore. Also, you'll be able to keep your important data on both drives, so you'll have sort of a backup when something fails. (A more robust backup solution will be better, but hey it's a start.)