Technically that is only adding to the prompt, which then becomes (your prompt + original response + your prompt 2), etc.

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.

Actually the replay wouldn’t be the same since it’s stochastic, and the more back and fourth you have the more chances for randomness to seep in. One could imagine by the fifth prompt or w/e the responses could have drifted enough that the subsequent prompts don’t make any sense.