I want to update my iPhone 7 to iOS 16

You cannot update to iOS 16 with an iPhone 7. You can update to iOS 15.7.2 but if you're really still on iOS 13 you might want to do that via a pc or Mac instead

Update your iPhone using a Mac with macOS Catalina or higher

On a Mac with macOS Catalina or higher, you will use the finder in order to upgrade your iPhone. Make sure to Back up your device before starting the upgrade process.

On a Mac with macOS Catalina or later, you will follow the following steps:

1. Open a finder window
2. Connect your device to your Mac via a lighting to usb A or a lightning to usb c cable
3. Select your device in the left sidebar of the finder window
4. click general, then click check for update
5. Click download and update.
6. If asked, enter your iPhone passcode

Update your iPhone via a Mac running macOS Mojave or earlier, or on a Windows PC

On macOS Mojave or earlier, or on a windows machine, we won't use the Finder to upgrade your iOS

Instead, we will use iTunes. Make sure to Back up your device before doing any update or upgrade to your phone.

1. Open iTunes
2. connect your device to the computer with an lightning to usb a or a lightning to usb c cable
3. Click device button in the iTunes toolbar
4. In the summary tab, click check for update
5. Click download and update, follow The on screen instructions
6. If asked, enter your iPhone passcode.

Not possible to update an iPhone 7 to iOS 16.

You can get it to iOS 15.7.2, but this won't work until you get the battery fully charged and other settings on the phone are checked. Fully charge the battery and try again. Report on any messages that you see or provide another screenshot if you are having problems.

NOTE that it says it is up to date with 13.6.1, which means it still has a beta installed. Until this is resolved it can’t be updated at all.

Delete the beta profile→How to uninstall iOS beta software - Apple Support