Second machine, different menu.
The create shortcut puts another shortcut on the desktop to open the web page directly, same as the Open option. seems quite redundant. 😉
1)The cut doesn't seem to work properly when I try pasting on a different folder shows the error below.
2)The delete just removes the icon from the desktop, then you have to go to personalize again and switch to picture and back to spotlight collection to get it back with the related menu.
Looks like they are still experimenting with different variations for this feature. 😎
Edit:
On this one the Icon and the menu just disappeared after an hour.
Now stuck with the first picture.