How can I update my iPhone 7 to iOS 16?

You can't. You are already on the furthest iOS your iPhone 7 is capable of running, which is iOS 15.8.3. iOS 16 is not supported on that and requires an iPhone 8 or later.

Not possible. You will need to purchase a device that has the hardware capable of running a newer version of iOS. Software has always outpaced Hardware ever since the first computer.