Conventional software support for the iPhone 7 was removed when iOS 16 was released. However, it still receives iOS 15 security updates (as of July 24, 2022.iOS 15 is the last version it will run). After Monday's WWDC presentation, iPhone 7 users shared their disapproval online over the lack of support for the upcoming iOS release. In addition, the fifth-generation iPad, which has the least powerful A9 chip compared to the A10 Fusion chip in the iPhone 7, is also compatible with iPadOS 16. Unfortunately, all the new features of iOS 16, including the update itself, will not reach customers who own a lot of old iPhones, the most notable being the iPhone 7 and iPhone 7 Plus.
The reasonable explanation is that the A10 Fusion chip in the iPhone 7 and iPhone 7 Plus is simply not powerful enough to run iOS 16 and all of its new features. It's hard to tell if the iPhone 13 is better than the iPhone 7 without knowing what your specific needs and preferences are.