FYI that is also how the numpy documentation is organized (see Array creation routines — NumPy v1.26 Manual for example). What I like a lot is the list with a short description, which gives the available API at a quick glance. It’s very useful both for modules and classes.
With the current documentation, I have to scroll the whole page to know what functions are available. I find navigating huge pages a hassle (see for example Built-in Types — Python 3.12.3 documentation).
Instead of rewrinting the whole documentation, I think a first step would be to add pages using sphinx.ext.autosummary, which would link to the existing documentation. I tried to generate those automatically by my result was not that great.
Some module docuemntations already include such tables in the introduction, maybe this could be generalized ? See statistics — Mathematical statistics functions — Python 3.12.3 documentation.
I think there are multiple ways to improve the status quo, with different levels of implication and rewriting. I just listed some of them here, I can try to add more details if needed.