iPhone 7 not updating to iOS 16.1.1

The last and final update for the iPhone 7 was iOS 15.8.3.

That is why your phone is saying that it is up to date. The iPhone 7 is not qualified to run iOS 16 or any other higher iOS version.

If you want to run iOS 16, you will need an iPhone 8, iPhone 8 Plus or iPhone X.

That is because your iPhone 7 no longer receives the latest iOS updates and you are already on the furthest it can run, which is iOS 15.8.3. You need an iPhone 8 or later to run iOS 16.