New error message when updating iOS

Okay, first of all do you have any other networks at home? If yes could you try switching to that network.

Could you try force restarting you're phone, heres a guide on how to Force restart iPhone - Apple Support (US)

Or else, you could perform a network reset, which would sadly remove all of you're networks, all of your Bluetooth device pairings, mobile network preferences, and stored VPN information. Settings < General < Reset < Reset Network Settings.

Wish it helps!

Thanks to @anypat's for this:

If you get a message that you are not connected to the internet while updating to a newer version of iOS, the following will help. This usually happens because an older version of iOS has been downloaded to your device but was never installed.

• Go to Settings | General | iPhone Storage
• Wait for apps to populate below
• Look for an iOS update, select it and delete it
• Go to Settings | General | Software Update
• Download and install the update

You should no longer get the message that you aren't connected to the internet.