How do I call the "Use as Fetch in Console" menu in the right-click options in developer mode of Firefox via JavaScript code?

Question

I want to make a bookmarklet that can call an API.

This API requires login to the site, so I must use the right-click option in Firefox developer mode in the Network Monitor tab: "Use as Fetch in Console".

Now I need to be able to call this right-click option with a javascript code and do the rest myself.