How to hide unused Product Configurations from Product Finder

We're using configured product structures. We have a mix of product configurations on a Model and predefined configurations applied to the root node. Clearly, predefined configurations can be removed simply by modifying the root and deleting those. 

For Product Configurations, created in the Variant Management app, how do I deprecate them so they don't show up in the Choose a Configuration dialog in Product Finder? I've promoted them to "inactive" but they still display in the "Choose a Configuration" dialog.

Is there a combination of Product Configuration lifecycle and a platform/user setting that then hides Product Configurations of a given state?

This is in 2018x, but I'm open to understanding mechanisms in 2021x (FD09) as well

Thanks for the guidance,