If you did not see each others new photos on both your iPhones and the deleted photos did not vanish from each others devices, at least one of your iPhones has not been syncing with iCloud Photos.
iCloud Photos may be enabled by default, when you upgrade to a new, major system version and have subscribed to additional cloud storage. So the current upgrade might have enabled iCloud Photos for all your devices.
What you are seeing is exactly the expected behaviour. The primary purpose of iCloud Photos is the syncing - for all devices using the same Apple ID the Photos Libraries will be kept identical and in sync. Your Photos Libraries should be identical on all your iPhones, iPads, and the computers.
To have different iCloud Photos Libraries, but to share your purchases, use different AppleIDs for iCloud and family sharing (Family Sharing - Apple Support) for the purchases and subscriptions.
You are aware, that keeping the photos in iCloud Photos does not suffice as a backup? iCloud Photos is really great as an off-site storage but is no full backup. You can get your photos back from iCloud, if your devices get damaged, the house burns down, the devices are lost or stolen. But you can still loose your photos by accidentally deleting them or making other mistakes. All your mistakes will instantly sync to iCloud Photos and update the library in iCloud. To protect yourself from user errors you need a backup like with Time Machine, where you have a backup history and can go back in time to recover older photos.
