I was surprised that Google's iOS app ignores iOS Photos' albums and favorites, and is practically the only app on my phone that doesn't allow me to share a picture into it from the camera/photos app.
I went ahead and wrote my own app that provides the share extension and hooks up to the Google Photos API, but even with that I can't write photos to albums that weren't created by my app. It seems like Google _really_ doesn't want me to get photos into Google Photos for some reason?