Why is my iPhone 13 screen dead after an update?

It is highly unlikely that an important update to system files would cause a hardware malfunction to your iPhone.

I recommend service.

Service Checklist:

• iPhone service pricing.
• Check AppleCare Coverage.
• Get your iPhone ready for service.

Click ▶︎ Start a Repair Request.

Need more help?

• Call 1-800-APLCARE.
• Contact Support.
• iPhone Support.
• iPhone User Guide.

Click ▶︎ Check Repair Status. 🔧

Good luck! 👋🏼😉

Unlikely that the update caused your screen to fail and is probably rather just a pure coincidence. First try a Forced Restart as this will delete any corrupt software files and re-index the file system.

• Press and quickly release the Volume Up button.
• Press and quickly release the Volume Down button.
• Press and hold the side button until you see the Apple Logo. 

If that doesn't help, there may be an issue with your screen digitizer in which you should make a reservation at your nearest Apple Store's Genius Bar or an Apple Authorized Service Provider. They will run diagnostics on your iPhone and determine what the issue is, then present you with your service options.

Genius Bar Reservation and Apple Support Options - Apple