You can get the un-redacted prompts via the OTel event logger[0], but unfortunately it won't give you responses. You could open up a GitHub issue to request that addition!
Disclaimer - I work at Anthropic but not on Claude Code, the team is responsive via GH issues though!
This is neat - I built something in a similar vein recently but less productized, good work!
I have a habit of moving around (thus changing doctors) and a lack of a history / being able to easily consolidate them has been a reoccurring pain. I recently had a full physical while in Thailand and there was some potential concern around my labs & some imaging --- of course, without history it was a "check again in 6 months!" which prompted me to capitalize on Gemini's PDF parsing abilities...