I frequently steer the AI mid convo though. So much so that I find it useless to share the original prompt. I don't know how best to capture that.
You could still capture it by recording only your prompts, the points in the conversation they were submitted at, and the starting parameters for the model. A replay would then produce the same results if your input was added at the same place in the conversation.
Granted I don't think the current tools do a great job of handling that.