How do I create a home HDD that works?

OK, see that play button symbol to the left of the - symbol? You need to click on the play symbol to mount the drive. To make this easier in the future, click on the GEAR icon, EDIT MOUNT OPTIONS, do this. Checkmark Mount AT System Startup. Checkmark in Show In User Interface

If you are still having issues seeing the drive in Steam after getting the drive mounted, then you maybe using the FLATPACK STEAM, in which case I have a tutorial on how to get that setup properly.

Hopefully this helps!