Hello deeptriest,
Thank you for using Apple Support Communities.
I see that you are having issues logging in to iMessage on your iMac because of issues with app-specific passwords. You may want to try to remove the related password and re-add it. This article addresses app-specific passwords:
Using app-specific passwords
This excerpt addresses managing them:
You can have up to 25 active app-specific passwords at any given time. If you need to, you can revoke passwords individually or all at once.
- Sign in to your Apple ID account page.
- In the Security section, click Edit.
- In the App Specific Passwords section, click View History.
- Click next to a password you want to delete, or Revoke All.
After you revoke a password, the app using that password will be signed out of your account until you generate a new password and sign in again.
Any time you change or reset your primary Apple ID password, all of your app-specific passwords will be revoked automatically to protect the security of your account. You'll need to generate new app-specific passwords for any apps you would like to continue using.
Best regards.