Our default facet controller is “Edit” at this moment, while the “Display” tab is the route most people will be using when configuring facets.
I suggest we follow core’s Field UI flow, thus:
rename our “Display” route to “Edit”, and use this as main route.
rename our current “Edit” route to “Facet settings”, and make it the 2nd tab instead.
In the facet overview page, we can still show the “edit” button this way, but it will link to the page most users actualy need (instead of having to use the dropdown).