These steps sometimes work: - close that account - exit and restart thunderbird - create account but do NOT include password (you will be prompted for it later)

The account was declared but remains empty. If I try to get messages, I get after repeating to Google my password and answering my phone "authentication failure". At the same time I can open my account directly on internet.

I suggest removing the account and starting over. Setting up gmail account is often problem-prone. Once the account is removed, start over and omit the password until the account is defined. Google should then prompt you for your id and password.