iPhone becomes unresponsive when trying to update software

iOS 15.8.4 is the absolute highest an iPhone 7 can be updated to. Since you have skipped a lot of updates on your phone, use your computer to update it. See how to do that here --> Update your iPhone, iPad, or iPod touch with iTunes - Apple Support Or, if you're using a Mac --> Update your iPhone, iPad, or iPod touch with the Finder - Apple Support

If you are unable to update OTA, then use a computer. If you can't update or restore your iPhone or iPod touch - Apple Support

You are trying to do an update using cellular data on a phone which is charged to less than 50%. If your phone can be updated, on an iPhone 7, you need to be connected to Wifi and your phone minimally charged higher than 50% or plugged in to charge.

You need a WiFi connection to update your phone if it's older than an iPhone 12.

Also, an iPhone 7 cannot be updated beyond iOS 15.8.4.

You have asked us to guess, among other things:

• Your iPhone model.
• Its current iOS version.
• What iOS version you are hoping to go to.
• What “hanging” means - what you see exactly.