We've discussed this as far back as 5.0, but it was not yet the right time to explore. Now that we have tools more clearly delineated, it's a good time to start looking at how we can split the block inspector between settings and appearance — appearance would generally be all the common block tools registered through supports, and setting would generally be block specific tools. The earliest mockups we had used a tabbed interface for this. There are some other considerations to discuss, including attribute types and UI slots for registering controls. We should assume by default <InspectorControls> are of role "settings".

Mockup:

See also: #42257, which could benefit from this.