Even the latest version of Thunderbird mail, present by default in Ubuntu 19.10 Eoan Ermine is distributed with bug that prevents this linux flagship mail app from connecting to Gmail account successfully.
When setting up IMAP connection with 2-Step Verification turned On it initially goes through all the authentication process and finally crashes with Authentication Failure.
Fortunately there is nice and easy solution!
Open Thunderbird Menu and go to Preferences > Advanced > Config Editor…
Search for ‘general.useragent.compatMode.firefox‘ and set it’s value to be ‘true‘.
Now try to establish connection to your Gmail account again and it should go through with no problems.
I’m not sure if it is Ubuntu’s Thunderbird distributed application problem, Mozilla’s problem or Gmail issue. Also can’t say how many users might be affected, but I think this is quite essential and either Ubuntu, Mozilla or Google should not let it like this.