In a normal org as a System Admin user, I can see the middle option here called "Assigned Connected Apps" (whether from a permission set or a profile), from which I can associate the connected app to the current profile/permission set.
I saw an org today where that middle "Assigned Connected Apps" option was not there, and I wasn't able to assign a connected app to the profile/permission set.
Does anyone know why that option wouldn't have existed on this org? Or how to assign a connected app a different way? They were on an Enterprise org and using a standard System Administrator profile.