Why does my iPhone say it's up to date with iOS 15.7 when trying to update to iOS 16?

An iPhone 7 cannot be updated beyond iOS 15.8.3. It doesn't have the hardware needed to run anything higher.

• If you have an iPhone 6S through 7, or SE 1st generation, you can update to 15.8.3

• If you have an iPhone 8 or X, you can update to 16.7.10

• If you have an iPhone SE (2nd generation or later), or XR through 16, you can update to 18.3.2

Go to Settings > General > Software Update.

This link will show you how to update your iPhone, iPad, or iPod touch using WiFi -

Update your iPhone or iPad - Apple Support

This link will show you how to update using your computer -

Update iOS on iPhone - Apple Support