iPhone camera defaults to share library

You don't say what version of iOS you are running on your iPhone, but there should be a switch in Camera and/or in Settings that determines which library receives newly taken photos.

For example, in iOS 26.0.1, Settings > Camera > Shared Library > Share from Camera, Share Automatically/Manually, and Share When At Home all set defaults. Camera has an icon in the upper left showing two heads and shoulders that switches between your Personal Library and Shared Library; it is yellow when set to Shared and white when set to Personal.