error 4013 on iphone x

Appears that you have tried everything possible to restore your phone. At this point, I would suggest that you make a Genius Bar appointment at your local Apple Store or Apple Authorized Service Provider to have them take a look and provide you with your options.

Ref: Genius Bar Reservation and Apple Support Options - Apple

See this troubleshooting document: https://support.apple.com/en-us/HT201444

Sadly all the cookie-cutter responses redirect you to a generic troubleshooting link (use the latest version of iTunes, different cables, computers, etc), which obviously doesn't work 90% of the time.

Having repaired hundreds of iPhones since 2007, I have found that error 4013 is usually caused by a flash chip/mcu failure due to damage to the main board by hard drops or liquid damage. Your best option to save all your data, is take it to a local independent repair shop, and have them clean up the main board with a chemically solution (should be no charge unless it works). As a last resort take it to an Apple store, and pay a bunch to have them replace it.

If you have an out of warranty phone with important info on it which is somehow not backup up to iCloud (or ran out of cloud storage), at least trying an independent repair shop does make sense, either that or loose all your data. Course if it's under warranty, by all means take it to an Apple store.

And what did Apple say when you contacted them as it directs you to at the end of the document?

I also had iPhone Error 4013 but managed to resolved it by changing my USB port while Updating my iOS. If the problem still occurs then try upgrading iTunes.

If you take it to an unauthorized shop and have them do what you are recommending, Apple won't replace it at all.

Your "last resort" is no longer an option once it's been tampered with.