An unknown error occurred trying to sign in to Apple ID on my Mac

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. Also try the Safe Mode. 

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

I have not seen a definitive solution for your problem. So, I suggest you use my search link in trying to solve it: an unknown error occurred apple. You will see a number of links that are, or may be, related to your specific problem. Several links related to my search claim fixes although they may not pertain to you specific problem.

If you want to contact Apple Support to deal 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 Be patient. Sometime this site is not fully functional.

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

Apple Support Twitter https://twitter.com/AppleSupport  There may be a wait of an hour or so.

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.