Okay, here is an update. There is something about that particular LAYER (or maybe how it was added to the Map) that is disabling the "Information" option in the New Map Viewer (I can see the source in Classic). Other layers I've added DO have the "Information" section as you've shown it in New Map Viewer. I'm looking into it further to determine what the difference is.
Okay, here goes...
If you add a layer to the New Map Viewer as a Web Service, you don't get the "Information" section as part of the "Properties".
And I don't see any way inside the New Map Viewer to see what the source of that layer is once you've added it.
Sure, AGOL Assistant is okay for that (but why should you have to leave the Viewer to get that info?). You can also open the map in the Classic Viewer where the Information functionality still works regardless of how the layer was added.
Rather than just unhelpfully dropping the Information section for a layer added as a web service, ESRI should have left it, but given the user some message "Sorry, this is a web service and our shiny new Map Viewer doesn't know anything about it".
I guess the lesson here is to try to exclusively use Add Layer and to avoid using Add if possible.