How to use iCloud Shared Photo Library with family members

The Bluetooth check is to see if any device belonging to one of the people connected to the Shared Photo Library is nearby (not necessarily in the picture) at the time the photo is taken (which can be tested quickly), in which case the photo is added to the library for everybody connected to the library to see and control. You can only own or be connected to one Shared Family Library, so you can't have one connection per family member.

In contrast to the quick decision that can be made about whether there is a family phone nearby justifying adding a photo to a Shared Photo Library, the decision of whether a face is recognized as a face at all can take quite a while. After that, it has to be matched against the array of known faces, and perhaps the photo will be added to the list of photos in your library containing that known face. That information stays local to your own Photos library unless you take manual steps to add the photo to a Shared Album or a Shared Photo Library (maybe with a Keyword or Description added), or