ios 16 does not want to install on my iphone 8 plus

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

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

See the following Apple articles:

Connect to Wi-Fi on your iPhone, iPad, or iPod touch

Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support

If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network

If your iPhone, iPad, or iPod touch won't connect to a Wi-Fi network - Apple Support

Low Power Mode is On.

Charge the iPhone & wait until the battery is fully charged (100%).

The Low Power Mode will turned off automatically.

Then you can perform the update.

You need about 6 GB device storage.

If they are On, turn Off Hotspot & VPN.

See the following Apple articles:

Update your iPhone, iPad, or iPod touch

Update your iPhone, iPad, or iPod touch - Apple Support (IN)

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 also need a cellular connection and you need to turn Low Power Mode off.

WiFi is needed to download, cellular is needed for verification.

What happens when you go to Settings -> General -> Software Update -> Download and Install?

Do you get any error message?