I got into a similar problems after moving my games from C:/ to D:/ to create space on C:/. The app wasn't able to see my game on D:/ and needed to install them back even if they were already on my PC. So I decided to do their job since it seems to be too hard for them to do (it took me like 2 hours to figure out...).

It's a way to change your installation directory and keep your games working if you already have some installed. You can then do the symbolic link trick for future installation if you’re using a custom directory.

1. move your games into your new directory and delete the old directory
2. open this site: https://sqliteonline.com/
3. on the site, click "File" at the top left, then "Open DB"
4. go to C:\ProgramData\Twitch\Games\Sql and open "GameInstallInfo.sqlite"
5. remove the "SELECT * FROM demo;" and paste this script instead:

UPDATE DbSet
SET InstallDirectory = "D:\Twitch\Games Library\" || (SELECT Id FROM DbSet db where db.id = DbSet.Id);

UPDATE DbSet
SET Installed = 1
WHERE Installed = 0;

6. before running the script, replace the "D:\Twitch\Games Library\" in the script by your new directory
7. run the script by clicking the "Run" button at the top
8. click "File" on the top left, then "Save DB"
9. replace the old file in C:\ProgramData\Twitch\Games\Sql with the download one

should be good, hope it help