Indeed, you are correct. The playground doesn’t use previous_response_id, it recreates the inputs.
I mentioned it because as we lack a documented guideline for why a stateful conversation that uses reasoning models (with or without reasoning summaries enabled) can’t be used by non reasoning models to continue it, playground was the closest to an “official statement”.
But I think we have to acknowledge that the responses API is slowly improving, it is much better now with code interpreter and other things that makes it a bit closer to assistants and “ChatGPT”.
Not “exactly” like them, but it is improving. We will get there eventually, hopefully.