Can't update iPhone 11 from iOS 16.3.1 to 17.5.1

My iPhone 11 has the update downloaded, but when it tries to install it spends a good few minutes on "Verifying update..." before failing with the error message "Unable to Verify Update | iOS 17.5.1 failed verification because you are no longer connected to the internet."

This is not true, the phone is still connected with solid signal strength to a wifi connection that sits at about 80mbps.

I have tried:

1. 1. Deleting the update from the phone and trying to download it again.
   2. Deleting all the network settings from my phone and then reconnecting to the wifi and trying again.
   3. Completely erasing the phone, and then downloading the update and trying to install.
   4. Connecting the phone with a cable to my MacBook Air with macOS 14.4.1 and attempting to download and install the update through finder.

• • • The error message it fails with in this case is "The software for the iPhone 'Will’s iPhone' was corrupted during download. | Disconnect and reconnect, then try again. Make sure your network settings are correct and your network connection is active, or try again later."

Having tried all this and still not succeeded, I'm not sure what else to try.

I should probably mention that the battery in the phone is not from apple, I had it changed recently. The iPhone throws a warning about the dangers of third party hardware, but it's never said anything about this preventing me from updating the software.

I wasn't going to go for a new phone yet, this one still works fairly well but there are now apps that won't work without iOS 16.4 or later, so that's an issue.