After you have loaded the Chrome Extension in the Browser , you will have to reload the site with the domain mail.google.com . After reloading you can open the console and check it will show the log.

Incase you do not see the logs , you can also check if the content script has been injected in the tab . Open the devtools and click on sources . Under it select content script . If your file is injected then it will be visible there.