My phone refuses to update manually

See this Apple article: If you see No Service or Searching on your iPhone or iPad

If you see No Service or Searching on your iPhone or iPad - Apple Support

If you still don't have a 'service' after that, see -> iPhone 7 Repair Program for "No Service" Issues

iPhone 7 Repair Program for "No Service" Issues - Apple Support

See this Apple article: If your iPhone, iPad or iPod touch won’t update

If your iPhone, iPad, or iPod touch won't update - Apple Support

You can do the update via PC, see this Apple article: Update software on iPhone, iPad or iPod touch in iTunes on PC

Update software on iPhone, iPad or iPod touch in iTunes on PC – Apple Support (UK)

If you have a Mac see this Apple article: Update your iPhone, iPad, or iPod touch with the Finder

Update your iPhone, iPad, or iPod touch with the Finder - Apple Support

You need good Wi-Fi connection.

If they are On, turn Off Hotspot & VPN.

To update over the air from the phone all of these requirements must be met:

• You need at least 6 GB of free storage
• You must be connected to a Wi-Fi network (and not a personal hotspot) unless it is an iPhone 12 or 13 series with an active 5G network connection
• The phone must be charged to at least 50%, and preferably plugged in so it stays above 50% during the update
• The phone must not be in Low Power Mode
• The phone must not be connected through VPN, and it may be necessary to delete any VPN apps and VPN profiles
• The phone cannot be in Airplane mode
• You cannot still have a beta version installed on the phone
• You cannot have a previous version that was downloaded, but not installed - go to Settings/General/iPhone Storage to look; if you find an iOS installer, delete it

If you can't meet all of them you can still update using your computer.