How do I keep a log of all AI prompts and responses? (automated)

I have to comply with GenAI rules imposed by a grant body. They require me to keep a log:

> This log should list: the model used, dates of prompts, the prompts themselves, the unedited output.

While this is borderline insane I'm actually curious to have that kind of archive. In the past I've selectively copied and saved responses, sometimes logs, sometimes even told the AI to update a document with the latest prompts and responses.

But it would be best if this were fully automated and complies to the rules above. Is there such a feature? Even if it's verbose debug logging.