3.16 won't open from the context menu

Can you describe which version you now have installed and in which folder you've installed that version?

Please also check the contents of those registry keys:

HKEY_CURRENT_USER\SOFTWARE\Florian Heidenreich\Mp3tag\Install\InstDir
HKEY_CURRENT_USER\SOFTWARE\WOW6432Node\Florian Heidenreich\Mp3tag\Install\InstDir

HKEY_LOCAL_MACHINE\SOFTWARE\Florian Heidenreich\Mp3tag\Install\InstDir
HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Florian Heidenreich\Mp3tag\Install\InstDir

It's no problem, if one of those doesn't exist.