How to update my iPhone 7 to iOS15?

You cannot pick and choose an iOS version. What you get is Settings > General > Software update > [All options are available here]

You need to correctly Identify your iPhone model - Apple Support

These are the iOS options based on iPhone Model -->

• iOS 16.3 —>
  • Chipset A11 - 8 / 8 Plus / X
  • Chipset A12 - XR / XS / XS Max
  • Chipset A13 - SE (2020) / 11 / 11 Pro /11 Pro Max
  • Chipset A14 - 12 Mini / 12 / 12 Pro / 12 Pro Max
  • Chipset A15 - SE (2022) / 13 Mini / 13 / 13 Pro / 13 Pro Max
  • Chipset A16 - 14 / 14 Plus / 14 Pro / 14 Pro Max
• iOS 15.7.3 —>
  • Chipset A9 - 6S / 6S Plus /SE (1st Gen)
  • Chipset A10 - 7 / 7 Plus
• iOS 12.5.7 —>
  • Chipset A7 - iPhone 5S
  • Chipset A8 - iPhone 6/6 Plus
• iOS 10.3.4 —>
  • Chipset A6 - iPhone 5
• iOS 10.3.3 —>
  • Chipset A6 - iPhone 5C
• iOS 9.3.6 —> iPhone 4S - Chipset A5
• iOS 7.1.2 —> iPhone 4 - Chipset A4

Know how to...

• Update Over-the-Air (OTA) —> Update your iPhone or iPad - Apple Support (IN)
• Update using iTunes/Finder —> Update your iPhone, iPad, or iPod touch - Apple Support (IN)

By using these instructions:--> Update your iPhone, iPad, or iPod touch

Specifically:

Assuming you're trying to update your device wirelessly, and bearing in mind that to perform such a procedure you need to connect your device to a reliable and fast Wifi Network with Internet access (no cellular data, unless you use a 5G network, no personal hotspot on your device, no VPN connections are admitted, no Low Power Mode enabled, and I suggest that you keep the device plugged into power during the whole update process), read this support article:--> If your iPhone, iPad or iPod touch won’t update (if you don't have a reliable and fast wifi network, "borrow" one from your relatives/friends/neighbors).

Also, make sure your device is NOT running a Beta operating system version. Should be this case, you need to remove it before installing any official iOS/iPadOS releases, as per these instructions:--> How to uninstall iOS or iPadOS beta software - Apple Support.

DO NOT forget to create a full backup of your device before updating its operating system, and keep in mind that, depending on the available storage on your device and/or on your wifi network speed, it might take 30-60 minutes to complete the entire update process.

If the issue persists or if the iOS version currently running on your device is very old (from your product list, it seems that the device is still running the old iOS 14), try to update it via computer (if you don't have a computer borrow one from your friends/neighbors, or ask for help at an Apple Store or Authorized Service Provider), then learn how to update your device manually if you're using a Mac with macOS Catalina or later, or if you're using a Mac with macOS Mojave or earlier or a Windows PC.

If you still get no help, contact Apple Support directly, using this link:--> Get Support

Regards

Giulio

You mightn't have enough space on your iPhone. You can always connect your iPhone to a computer running the latest version of iTunes via a lighting cable, click the iPhone logo that appears in the top left hand corner, navigate to software update and check it that way. Still need help? Check out this website - If your iPhone or iPad won't update