Need to test the freshchat app directly from freshchat environment by sending a message. We already tested the app using simulation method as mentioned here in this link End-to-End Testing do we have any other testing method,
Edit: Post edited to remove the screenshot having credentials.
You can publish the app as custom app & test in your freshchat account. Since the custom apps are specific to your account it should help you test real-time the same you’ve verified via simulation.
You can read more about custom apps here - Custom Apps
To check logs,
Go to gallery → Manage Apps → Custom apps(tab) → click on the settings dropdown of the app you wish to check → view logs