And, until a quick discussion with Mark Uraine, one of Gutenberg’s designers, on a GitHub ticket, the idea did not seem to even be on the table

I'd say patterns should be present anywhere blocks can be inserted! Specific categories of patterns might be more relevant for some specific areas, but for widgets it should likely just show all patterns.

Another thing that should be attempted soon in the plugin is augmenting block rendering server-side with the default widget classes to see if theme compatibility can be increased out of the box. Thanks for the thoughts!