Make sure cookies are enabled in Thunderbird:

• Select 'Menu app icon' > 'Options/Preferences'
• In 'Options/Preferences' left Pane select Privacy & Security
• Select checkbox 'Accept cookies from sites'

Menu app icon (3 horizontal lines) > 'New' > 'Existing Mail Account'

Enter Name

• Enter email address
• Enter Password
• Select checkbox to remember password
• click on 'Continue'

Thunderbird will auto set up as an IMAP mail account using Authentication Method OAuth2

• click on 'Create Account'

You will then get a prompt from gmail to confirm you really are you and to allow Thunderbird access. Follow instructions. Then a token is created and saved in Thunderbird.

https://support.mozilla.org/en-US/kb/automatic-account-configuration

If set up as IMAP accounts then emails are stored on server and you use IMAP accounts to show exactly the same as on server, so you can access using more than one computer to see the same.

Info on IMAP Synchronisation: https://support.mozilla.org/en-US/kb/imap-synchronization