docs: index cleanups

Here's some cleanups to index.rst (and some related files) I'd been wanting to do since the sphinx-conversion.

Most of this is about making the initial page more approachable, by not throwing a lot of history and otherwise needless details at the reader. There's also some changes trying to update and clean up the front-page a bit.

Some of this is about trying to restructure the toctree-stuff a bit, to avoid the hacks needed because of contents.rst. In the long run, we should probably restructure the docs to be a bit more hierarchical, in line with how Sphinx documentation is intended to be written.

That toctree-stuff hasn't really gotten far, though. So if people aren't convinced yet, I'd be happy to move that to a separate MR on top instead.