Why does my iPhone only let me update to 15.7.9

For an iPhone 7, that would be the latest update. If you were expecting iOS 17, iPhone 7 is simply not capable of running it. It wasn't capable of running iOS 16 either. Your iPhone is pretty old at this point and it lacks the hardware required to use the newer iOS versions.

The iPhone 7 is not compatible with iOS 16 or higher.

Because an iPhone 7 doesn't have the necessary hardware to run anything higher.

Because you have iPhone 7