Update "copy branch" shortcut to click on MR sidebar button

What does this MR do?

Updates the "copy source branch" keyboard shortcut (originally implemented in !36338 (merged)) to trigger a click on the button in the MR sidebar instead of the button in the MR widget.

This MR effectively undoes !36338 (merged) and re-implements this behavior in a new location.

See #247177 (closed) for more details about why this is beneficial.

GIFs

When the sidebar is expanded:

When the sidebar is collapsed:

Notes

When the shortcut is triggered, the tooltip is shown, but it is never hidden. This is the same behavior that occurred when clicking the original button in the MR widget.

Related to #247177 (closed)