I wonder if fairly standard reviews might be helpful here. 1-5 stars, with text, and perhaps also links to issues if there are problems and an opportunity to share "used at $company" for endorsement.

Or perhaps just a built-in "endorsement" feature, which companies can use to indicate that they use a project and find it valuable, perhaps listed on the sidebar. Could also segue into paid sponsorship and support.

Insofar as GitHub provides package management, they could also prompt companies to endorse the packages they use.

All of this might get annoying, nasty, or inauthentic, of course. Would need to be careful...