On Windows 10 global hotkeys of nonelevated apps do not work from elevated apps
Solution 1:
That's by design in Windows' User Account Control: it would be a potential security issue if any application were able to spy on key presses in applications with elevated permissions.
If you trust a specific program using a hotkey, you can configure it to always run with administrator privileges. As you're mentioning Greenshot specifically, that's one of the workarounds we suggest for this behavior.
Disclosure: I am member of the Greenshot team.