Can you just select the page where you inserted live chat with shortcode as Messages Location?
Installing messages location is required for correct plugin functionality, including messages notifications, email notifications and many other things.
It’s not added directly in a Page. It’s added indirectly.
In My Account, I created a new EndPoint.
In this EndPoint, I created an HTML Block.
In this HTML Block, I added the shortcode.
The setup works, but is not detected.
You need to point plugin to that location, otherwise notifications will not work correctly, etc.
You can check more here: