Based on feedback from:
Redesign/refine block inspector header (the block card) for patterns, claim back more room with changes to spacing, layout, text-wrapping.
Make header icons consistent with whatever the list view and toolbars show.
Here's what the header looks like now:
With less indentation and padding:
Icon consistency is being looked at over in:
Related
Just adding as a note: another idea is to eventually move such actions to "pinned-to-the-footer floating actions" or “Quick Actions” that are docked it to the bottom of the DataForm column. This relies on DataForms improvements so only mentioning.