My complete reasoning, notes, errors have never been part of the commit. I don't see a valid reason on why the raw conversation must be included. Rather I have hooks (or just "manually" invoked) to process all of it and update the relevant documentation that I've been putting under docs/.
If you also ensure the AI writes relevant (and correct) docs, and also code comments and commit message, then I agree there is not much need for extra info, e.g. prompts / session distillation. I am not sure that that is the case currently (though we might be getting there soon at least in some cases).