This is a solid and very interesting paper! The authors were kind enough to publish the complete prompt for it (appendix B.1 on page 18), so anyone can try their approach with any LLM and see the results.

It says to read the complete history. Would that be analogous to reading all of one's chat threads, or just the history of the relevant chat thread that it's a part of?

So its more like a harness (like Codex etc) on top of any existing LLM?