Apple id an unknown error occurred

Are you running any anti - virus programs? Using a VPN?

Try setting up another admin user account in System Preferences/Users & Groups to see if the same problem continues. Please post back on whether or not this worked. Also try the Safe Mode. Please post back on whether or not this worked.

Isolating an issue by using another user account    

Safe Mode - About.       

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply. After pasting the report in a PasteBin page, go to the top of the page, and copy the address in the URL bar. Paste that in a new reply.        Pastebin.    

Etrecheck – System Information.      

Web site version if required.  https://etrecheck.com

See these documents. I cannot guarantee a solution though.

Verification failed https://discussions.apple.com/thread/8321958

Apple ID Verification Failed: Unknown Error Occurred https://discussions.apple.com/thread/8343214

Verification failed : There was an error connecting to apple id server https://discussions.apple.com/thread/7238348

Error Connecting Apple ID, Verification Failed. How-To Fix https://appletoolbox.com/error-connecting-apple-id-verification-failed-how-to-fix/

How To Fix Verification Failed Error Prompt After Update To iOS 13 https://www.ikream.com/how-to-fix-verification-failed-error-prompt-after-update-to-ios-13-36692

If you want to contact Apple Support for help with your problem, see:

Get a call from Apple support to help solve your problem using this link https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0245&symptom_id=23362

Apple ID Support https://support.apple.com/apple-id

Apple ID account security for country-specific and region-specific help https://support.apple.com/en-us/HT204169

Get Support: We’re here to help https://getsupport.apple.com/. Go through the options to find the best one.

You are welcome. Something in your normal user account is affecting the connection. Try booting into the Safe Mode in your normal user account as posted above.

You are welcome. Easy fix.