Hi margo2018,
Thank you for using the Apple Support Communities! We understand you are receiving an 'unknown error occurred' when attempting to sign in to your Apple ID on multiple services on your Mac, since migrating from your old Mac. We'd like to help.
You did a great job ruling out an issue with your Apple ID credentials, by testing that you could sign in on the Apple ID website. Let's have you try the steps found in these related articles next:
If you can't connect to the App Store, iTunes Store, or other Apple services - Apple Support
If you can't connect or sign in to iCloud - Apple Support
Be sure to try connecting your Mac to a different network as well, to rule out network-relates causes. This could mean connecting to Ethernet, or a different Wi-Fi network.
If the issue remains, we'd like you to create a new user account for testing purposes: Set up users, guests, and groups on Mac - Apple Support. Once the new user is created, log into that user and see if you can sign in any where with the same credentials.
Keep us posted. Regards.