Thanks for your encouraging message, Ralf.
Something that I can notice immediately is that the interface of the docs looks a bit outdated and maybe it can benefit from an update (or replacing it with another template), in order to make it a bit more responsive. It is true that when you program you usually work on a big screen, so a responsive web page may not be an absolute requirement, but still it may be nice to be able to read the docs from a tablet or smartphone.
Unfortunately I am not familiar yet with Sphinx, but I hope that it can be integrated with Jekyll or Hugo, and then one of their templates can be used.
About the content of the User Guide etc. I don't see any obvious improvement that is needed (maybe because I have not read them yet). One thing that may help is making the code examples interactive, so that the readers can play with them and see how the results change. For example this may be useful:
https://github.com/RunestoneInteractive/RunestoneComponents
The two changes that I have suggested above seem more like engineering work (for improving the documentation infrastructure), than documentation work. For making a content that can be easily grasped by the beginners, I think that it should be presented as a series of problems and their solutions. In other words don't show the users the features and their details, but ask them to solve a simple problem, and then show them how to solve it with NumPy/SciPy and its features. This would make it more attractive because people usually don't like to read manuals from beginning to the end. This is a job that can be done by the teachers for their students, having in mind the level of their students and what they actually want them to learn. I have noticed that there are already some lectures, or books, or tutorials like this. This is a creative work, with a specific target audience in mind, so I can't pretend that I can possibly do something useful about this in a short time (2-3 months). But of course the links to the existing resources can be made more visible and reachable from the main page of the website.