In case you weren't able to fix this problem and for anyone else experiencing the exact same problem (like I did) you can try the following (if on Windows):
DISCLAIMER:
I am in no way affiliated with EA!
You do all of this at your own risk. I can not guarantee this will work for you and also can't say for sure you will keep your save files when doing this. Proceed with caution and make sure you understand these steps and follow them precisely before continuing!
Navigate to the installation folder of the game in question. There you should have a folder called "__Installer". Open it to find several files including "Touchup.exe", "Touchup.dat" and "installerdata.xml". Touchup.exe seems to be some kind of setup.exe and Touchup.dat might provide the setup with all the information necessary but I'm not sure about that.
Inside this folder you need to hold down Shift and right click on an empty area. Make sure to not click on a file or else you won't get the desired menu.
After shift + right clicking you should see a menu with one of the options being "Open PowerShell here" or similar. Click on it to start PowerShell which is a newer version of the Windows CommandLine.
Inside PowerShell enter the command
".\Touchup.exe install -repair -locale <locale> -installPath "<path to your game>" -autologging"
and replace <locale> with your desired locale code (e.g. en_US) and <path to your game> with the path your game files are already in (e.g. C:\Program Files\EA Games\Jedi Survivor).
Make sure to enter the full command without quotation marks at the start and end but to put the game path inside quotation marks (e.g. "C:\Program Files\EA Games\Jedi Survivor"). Double check the full command (it should be something like .\Touchup.exe install -repair -locale en_US -installPath "C:\Program Files\EA Games\Jedi Survivor" -autologging) and then hit Enter.
You won't see anything happening except maybe the windows loading circle but in the background EA's Touchup.exe will repair/re-verify your existing game files and after fully closing and opening the EA App your game should hopefully show up as installed. In case it doesn't the file "installerdata.xml" I mentioned earlier might give you some clues about what went wrong.
This also works if you can't start the download of a game you already downloaded but the EA App doesn't recognize because you don't have enough space on your hard drive to download the whole game again - which is what happened to me with Jedi Survivor (I simply didn't have another 150 GB of free space to start the download so the EA App would verify my existing files).
Hope this helps 😉