The save shortcuts blurred document.activeElement before clicking. With
focus on an input inside a shadow root that is the host, and blur() on a
host that is not itself focused does nothing (spec, Firefox), so a plugin
field type committing on the native change event lost the typed value.
The shortcut now focuses the button first, as a pointer press does, which
unfocuses the inner input in open and closed roots, and gives focus back
to the innermost element reached through open shadow roots.
