"13.0 profile"? AFAIK, it's just beta profile.I agree. Whatever shows up will most likely be a 13.0/13.1 17Axxx build with a name being whatever Apple wants to call it. Being that 13.1 in its current form is technically a 13.0 build using the current 13.0 profile and versioning scheme they can roll out whatever they want and it will update all users on build 17A5831c or lower. If they choose to label it 13.0 or 13.1 is debatable. IF they label it 13.0, I suspect the next 13.1 beta build will move to the normal 17Bxxxx build versioning to reflect a true x.X update.
IIRC, on previous versions of iOS, I just installed my beta iOS profile, and after the OS was updated to GM, if I didn't delete the profile, then I would get the x.1 beta update reminder eventually.