If you want to remove Pin to Start from the right-click context menu in Windows 11/10, then delete the PintoStartScreen Registry key.

If you enable this setting, the Start Menu will either collapse or remove the all apps list from the Start menu. Selecting “Collapse” will not display the app list next to the pinned tiles in ...

Applications like File Explorer and the Start menu search panel 'talk' to the new data store, thus their "Pin to Start" options try to pin tiles to the Windows 11 Start menu, not the Windows 10 one.