At the end of May, 2022, GMail discontinued use of standard authentication methods for POP3, IMAP, and SMTP connections. The available OAuth2 authentication mechanism in the latest SeaMonkey and Thunderbird for the OS/2 platform is unable to properly complete the authentication procedure with GMail, and will leave the application in a hung state.
There are several methods to work around this, but perhaps the easiest is simply to generate what Google calls an app password, which is, quite simply, a 16-digit passcode which gives a non-Google application or device permission to access your Google Account.
Once you have generated the app password, copy it to your clipboard. Open SeaMonkey Mail or Thunderbird, and access the server settings for your GMail account. Ensure that the authentication method is set for Normal password (Google will not accept encrypted passwords for this). Make the same change for the GMail SMTP server. Note that in both cases, SSL/TLS should be selected for the connection security, and specifically not STARTTLS. Close the settings dialog and attempt to access the account. You should be prompted for a new password. Paste the app password into the prompt.
To configure a second system to access the same account, simply paste (or type) the same app password. This technique should work for other mail clients, as well.
For questions, there is an informative discussion in the OS/2 World forum on this very topic.