We want to make an attribute searchable for shoppers but don’t want it to show up on a search or browse page. Is it a facet or metadata?

This attribute will be a metadata point. There is no need to configure it as a facet if you do not intend to make it a filter on search and browse pages.

For example, your shoppers can search for "lactic acid" to return all items that contain it, but they will not see a specific filter to view items containing it.