Is it possible to insert 3D buildings into Story Maps? The types of 3D buildings I'd use in CityEngine. Or even just a scene in ArcGIS Online, not a webscene you'd export from CityEngine, but the scenes (content>create> app, map, scene)?
Yes, Map Journal maps are only 2D (same for every StoryMaps and template in ArcGIS Online) but you can integrate virtually any content in Map Journal through another web application.
See for example that Journal that include some web scenes http://story.maps.arcgis.com/apps/MapJournal/?appid=4c77a56bbcd743b69232cf3fd9c7a61c and that blog post for the procedure Using 3D web scenes in Story Maps | ArcGIS Blog
But can I make the static reference map display 3D buildings, like in ArcPro, or could I just make the main stage a web scene and the side panel would have pictures/other media?
I am not sure what you mean by the static reference map but yes the links I sent you are to include web scenes in the Main Stage. You can also include web scenes in the Side Panel through the text editor inline media features if you want but that's not so common as the space is limited and most of author will only include text and images.