I hope I am understanding the issues frustrating you correctly. If the following doesn’t address your concerns, please let me know what I am missing and I will try to do better.
Prezi Next has gone a different route with regards to setting the path than Classic. We have made it easier for new users to create something great without needing to understand what a path is, but we also feel still offers flexibility for customisation. We are actively working on both making it easier to create a journey through your content, and have the flexibility to tell the story you would like to.
In the meantime however, if I am understanding some of the specific issues @Gerald_Gantschnigg visualised (which the original poster @Rachel_Benbrook seemed to agree with), the following should help.
The overview sidebar on the left is primarily intended as a way to manage your content, not your path. You can reorder topics there, but as you can see it doesn’t do a good job of adjusting path in the way you would like to. We should do better here.
Instead, to modify the path, we encourage you to interact directly through the canvas, by dragging and dropping. I created a short clip to illustrate how this would deal with the scenario in your first gif @Gerald_Gantschnigg.
As you move topics above the path, it shows the white circle to illustrate the “landing zone” for that topic. Topics then snap to the path, but can subsequently be moved to wherever you want them. The logic behind our snapping probably isn’t perfect yet, but we are tweaking it. I suspect this is the source behind the frustration @Rachel_Benbrook mentioned in the first post.
Finally, the behaviour @Gerald_Gantschnigg mentions in the final post looks like a bug. Our teams will try to reproduce and fix.
Please let me know if the above helps somewhat.