After installing the GOTY version there was no shortcut anywhere to start the game. I found the Witcher exe file in bin/x64. I was able to set a shortcut to the desktop and the quicklaunch but when setting one to the start menu it becomes invalid and doesn't work.

Windows 10 is a pain in the arse. Here's how to do it:
https://www.windowscentral.com/add-app-shortcuts-start-menu-manually-windows-10