We love these self-answered posts
Out-of-the-box, uncustomized Story Map Tour doesn't support popups on the supporting layers, like study area polys or hiking trail lines, in the web map. We did this to keep things simple in the limited space in the Map Tour and (dare I say it) a lot of popups in web maps aren't configured by the authors to look really great.
For place based story maps though where you want to show popups for supporting layers, the Story Map Shortlist does support popups for these layers. One of the issues with this though is that some Shortlist authors are including supporting layers, like county or city boundaries, that don't have good looking popups, so perhaps they are not realizing that these popups are appearing for their readers. They could just turn off the popups for those layers in the web map if they aren't needed.
If you want total out-of-the-box freedom for the popups, supporting layers and map extent/appearance for your place-based Story Map project. you could try using Story Map Journal and authoring each section manually. See this cool example from New Zealand.
Rupert