In the meantime, one thing that comes to mind is that simply embedding the whole contents of the webpages after scraping them didn't yield very good search results. As an example, an article about Python might only mention Python by name once. I found that trimming extraneous strings (e.g. menus, share links), and then extracting key themes + embedding those directly yielded much, much better results.
https://arxiv.org/abs/2212.10496
https://github.com/texttron/hyde
From the abstract:
Given a query, HyDE first zero-shot instructs an instruction-following language model (e.g. InstructGPT) to generate a hypothetical document. The document captures relevance patterns but is unreal and may contain false details. Then, an unsupervised contrastively learned encoder~(e.g. Contriever) encodes the document into an embedding vector. This vector identifies a neighborhood in the corpus embedding space, where similar real documents are retrieved based on vector similarity. This second step ground the generated document to the actual corpus, with the encoder's dense bottleneck filtering out the incorrect details.