You did not manage to open the Google Picker. That is most likely due to the third-party cookies being disabled. Indeed, Form Publisher uses those to communicate with Google Picker.
To use the Google Picker inside Form Publisher, you only have to enable third-party cookies. Depending on the browser and your browser version, you will find this option at different places.
Please copy this URL in your browser :
Then be sure to disable the option to block third-party cookies:
You can check this article to enable third-party cookies.
Continue your configuration
Once you've authorized third-party cookies, restart the add-on's configuration, or open the sidebar where you encounter the bug.