Implement some kind of caching

When running a documentation build multiple times, even if all the rest is cache, the full API docs get re-generated. We should have a way to cache this, though I don't know yet what the best way to do that is.

Start by tracing how the Sphinx extension regenerates full API documentation during repeated builds and review the available documentation-build caching mechanisms. Done means unchanged builds reuse the generated API documentation while still reflecting source changes.

Written by the indexing model from the issue text.