iPhone 17 SE stuck at Verifying Update screen

Force-restart the iPhone, and start over.

1. Press and quickly release the volume up button.
2. Press and quickly release the volume down button.
3. Press and hold the side button until you see the Apple logo (this might take longer than 10 seconds), and DO NOT SLIDE TO POWER OFF.

The operative word here is QUICKLY for the first two buttons, then a long hold for the SIDE button; and try it a couple of times, the timing is a little tricky. If done correctly this will always work unless the phone has a hardware problem. 

An iPhone must be connected to the internet to verify a software update before it can be installed.

If you connect to Wifi, doesn't necessarily mean you are connected to the internet. --> Internet not available WiFi and Cellular … - Apple Community

Wi-Fi Assist is on by default. This will automatically switch to Cellular Data if the device is not connected to the internet.

About Wi-Fi Assist - Apple Support