Photos from my current phone are showing up on one of my older phones

When I upgraded to the iPhone 12, I gave my 9-year-old granddaughter my old XS Max. Problem is that the phone is essentially registered to my email address. Whenever I take photos or videos, they are showing up on her phone as well. Worse, if I delete them off her phone, they are also deleted from mine as well. When I go to turn off iCloud Photos in settings, it asks if I want to download a copy of my iCloud Photos to my current phone.

Why would I want to do that? I want to keep my backed-up photos in the cloud, and not have to download them to my phone. I just want to protect the photos on my phone and not worry about my granddaughter inadvertently deleting photos on her phone, and consequently, from mine.