This is a new workbench extension which logs you into the Workbench in one click.
Updated, tested and works for Google Chrome and Microsoft Edge.
After you install you need to set the workbench base url, if the login url is https://workbench.developer.com/login.php then enter base url as https://workbench.developer.com
If you need to access the Options menu in the future, right-click on the toolbar button.
This extension is not compatible with workbench.developerforce.com server due to terms of service agreement and login CSRF requirements.
Host your workbench server by following this link: https://github.com/forceworkbench/forceworkbench#getting-started and provide the base url.