The Partner Collaborations Settings have a toggle that allow the partner org to search for members of your org, but users must still have a public profile in order to be found when partner group manager is searching to add them to a partner’s group. Even if the user has the “join external groups” permission, they can’t be found by group managers searching for them.
These two things are contradictory. If we give partner explicit permission to search for members, then the user profiles visibility requirements should reflect that.