Trying to update my Iphone 13 without success and my error code (4000) is not listed. What am I to do?

Have you try a different Apple USB cable?

Try this -> Go to Settings ->

(1) Display and Brightness  -> Auto-Lock set to Never.

(2) Face ID & Password  -> turn Password Off

Remove VPN if necessary.

See this Apple article: If you see an error when you update or restore your iPhone, iPad, or iPod

If you see an error when you update or restore your iPhone, iPad, or iPod - Apple Support (SG)

Guess you use a Windows PC, if so check the AV & Firewall you use on the PC. 

Disable all AV & Firewalls temporarily while you restore & update your apple device.

If they are On, turn Off Hotspot & VPN. 

Have you check the AV & Firewall you use on the PC?

And disable all AV & Firewalls temporarily while you restore & update your apple device?

If they are On, turn Off Hotspot & VPN.