If you used a Story Map Series and set the point layer pop-up to show when you move through the story, that would expose the attributes. Make sure you, within the web map, properly configure the pop-up to suit your narrative needs.
Also, using web app builder, you could use the Info Summary widget to create some level of detail in a panel.
I have to admit, like the capabilities to expose attributes in a details panel within dashboard, it would be nice if that same feature was available when creating a Story Map - very useful for dynamic content.