Unknown error when signing into my Apple ID and iCloud.

Activate safe mode https://support.apple.com/en-us/HT201262

Open system preferences > click on Apple ID icon , again click on overview , an error will show update your Apple ID settings click on continue , enter your Apple ID and password , in the same way click on name , phone , email .

If you upgraded the Mac OS from previous version to Mac OS catalina , and in the previous version secondary account was activated , it's better switch with two factor authentication .

When Mac is in safe mode enter the updated password in appleid.apple.com and www.icloud.com

Note : when ever you change Apple ID or its password it has to be updated in Mac system preferences see the article https://support.apple.com/en-in/guide/mac-help/mchl3f671010/mac

Just an informative article for keychain , only read it https://support.apple.com/en-in/guide/mac-help/mh36817/mac

The keychain paragraph , deleting the keychain folder from user library > preferences has a draw back it will mismanage the .plist arranged in alphabetical order , and never to be applied by a Mac administrator , you are not apple support advisor and can set the plist once again alphabetically and resetting the iCloud Keychain will delete the stored password , so when ever pops appear for icloud keychain , an iPhone is used and signed in with same Apple ID and password that was in Mac and set from iPhone and Mac simultaneously

The old apple account that you created that you signed in with Apple ID and password will be active unless you delete permanently from web server and iCloud server https://support.apple.com/en-in/HT208504

Also it depends what credentials you have in your records like zero credentials that also showed Apple ID doesn't exist , erasing the hard drive and reinstalling os is far better than archive installation , as every system file , every application is installed as fresh , the system is just new https://support.apple.com/en-in/HT204904

Do you get any sort of message when you try to sign in on the Catalina machine? Can you sign in to other accounts requiring an Apple ID using the Catalina machine. Try signing in to your account at Apple.com with it. If no success, try using another browser. Your Apple ID obviously works since your signed in here on some device. Do you have two Apple IDs?

See the document below. "The author says: "A corrupt Keychain can prevent multiple services from logging in, including iCloud. Here is a way to figure out if your Keychain is the cause of not being able to login to iCloud."

And, the author provides a solution.

Verification failed An unknown error occured https://apple.stackexchange.com/questions/378183/verification-failed-an-unknown-error-occured-on-sign-in