Hi Regina,
In the new Quick Report lots of changes and enhancements have gone in and you can read and learn about it in this blog post: https://community.esri.com/groups/appstudio/blog/2017/01/02/updates-to-quick-report-in-13
For the map related question now the Quick Report template supports WebMap. In the settings please provide a publicly available WebMap id and the template will show the map (as shown in the video above). So you do not need to copy over any files from the older version.
I ran your application in AppStudio and was able to see topographic map in the map page (see attached screenshot). In your application the web map id is d5e02a0c1f2b4ec399823fdd3c2fdebd and its showing the correct map. If you want to use your own web map with your layers in them just replace the id in appinfo.json or using settings tool.
Hopefully this helps. If I have misunderstood your problem please records a short video and post it.