My Sims 4 says I don't have the game installed

@mystiicql  It's possible your antivirus has quarantined Sims 4, or at least the .exe, and that's why the EA App doesn't recognize the game as installed.  Normally you could tell the App to redownload the game to the same location, and the App might simply verify the files' presence and finalize the install process, but that doesn't always work with so little free storage.  So one fix here would be to clear more space, at least 20 GB plus a little extra for overhead.

If that's not possible or would be inconvenient, you could delete the Sims 4 program files instead and let the App download from scratch.  By default, the game would likely be installed in one of these locations:

C:\Program Files\EA Games\The Sims 4

C:\Program Files (x86)\Orign Games\The Sims 4

You may have installed in a custom location, in which case look there instead.  But do NOT delete the Sims 4 folder in Documents > Electronic Arts: this holds your saves and other user data and is separate from the program files.

Once you empty the recycle bin and restart your computer, you should have enough space to download the game again.