After uninstalling the launcher, make sure to check that no files are left behind. You will want to look for and delete these folders as well (if they exist):C:\Users\\AppData\Roaming\Paradox Interactive\launcher-v2
C:\Users\\AppData\Local\Paradox Interactive\launcherpath (should be gone)
C:\Users\\AppData\Local\Paradox Interactive\launcher-v2 (should only contain logs)

Then start the game through Steam and the launcher will install itself again. If you're still having issues after doing that, then I really recommend contacting Paradox Support, so they can help you get things running and log any bugs that might need fixing.