If you're experiencing issues with setting up Gmail's 2-step verification, there are a few things you can try to resolve the problem:

Double-check your phone number: Ensure that you have entered your phone number correctly during the setup process. Verify that the country code and phone number are accurate, and check for any typos.

Check your network connection: Make sure you have a stable and reliable internet connection. A weak or intermittent connection may cause issues with receiving the verification code.

Request a new verification code: If you haven't received the verification code, you can click on the option to request a new code. Gmail usually provides multiple options for receiving the code, such as via SMS, voice call, or using a Google Authenticator app. Try selecting a different method to receive the code and see if it resolves the issue.

Is a possible work-around to copy Thunderbird settings from the home computer to the laptop?

Then how did you get 2-step authentication going on the home computer without a cell phone?

You can install an authenticator app, e.g. Google Authenticator, on your cell, link it to your Google account, and select the authenticator method when prompted for the second factor.