TriSarahtopsfaw You can install the game wherever you want. It will load more slowly from the HDD, but if that doesn't bother you, there's no reason to move it back to the SSD.
I think the issue here is that you're looking for your saves in the wrong location. The game's program files (what the EA App installs) and your user data (saves, mods, etc.) are completely independent. The latter will always be in Documents > Electronic Arts. Here's how to find the full path to the user folder:
https://sims4.crinrict.com/eng/2018/07/how-to-find-your-user-folder/
This folder can stay on your SSD, and if you have a lot of custom content, you'll definitely get faster loading times with the data on the SSD. But if you'd like to move it to the HDD anyway, you'll need to create a symbolic link. Here's how:
https://crinrict.com/blog/2020/02/moving-windows-documents-folder-to-external-drive-via-symbolic-link.html
The one caveat is that the user data cannot be in the same location as the program files. So for example, if your game is installed to D:\Games\The Sims 4, your user data can be anywhere you want, except directly inside D:\Games.
If you get an error when trying to create the symlink, please post a screenshot of the Command Prompt window showing the command you used and the error that resulted.