Changing the Apple ID on an iPhone without losing my photos

The bit that catches people out is Optimize iPhone Storage. If iCloud Photos is on with that setting, most of what you see on the phone is just a small preview and the full photo lives in iCloud. Sign out and those previews go. So before anything else: Settings > Photos > Download and Keep Originals, then leave it on wifi and charging until the library has finished downloading (the bottom of the Library tab tells you). Copy everything to a computer as well, just to be safe. Then Settings > your name > Sign Out. When it asks what to keep on the iPhone, switch Photos on. After you sign in with the new Apple ID you can turn iCloud Photos on there and it uploads the lot.