As in the title, I have a builder with a silk-touch quarrying shape card, but only the borders of the defined area are actually being quarried.

Select 'Solid Box' as shape instead of just 'Box'

Thank you, just as a suggestion, could you make that the default shape for quarry cards? It seems to me that it would also be the most commonly used one you see.

Yes, you are not the first one hitting this issue. It is perhaps not 100% clear :-)