Unlike most native controls text boxes do not show a context menu on right click. There is one exception: When right-clicking on a TextBoxBase_NSTextView while it does not have focus the macOS context menu is shown. It does not work when right-clicking after the control was activated.

Also Apple+C/V/X shortcuts don't work.
I'd be happy to trying adding the functionality. However, I'm wondering if overriding the mouse button and key down events and adding the required calls here is would be the right approach.
@filipnavara Can you share any hints?