Unable to link Gmail accounts into Apple Mail - Authorisation Error

I am operating macOS High Sierra v.10.13.6 - software updates are current except for incompatible items. Apple prompted me to change numerous passwords due to a data leak. I changed the passwords on some gmail accounts however I am unable to synchronise these accounts into Apple Mail - when prompted to add password I receive the message attached. I am able to log into the gmail accounts through googlemail but not through Apple Mail. I have tried all the suggestions online and through the gmail accounts - security etc. I have deleted the accounts on Apple Mail but cannot add them back because of the Authorisation Error.

Any suggestions?