Congrats on discovering what "thinking" models do internally. That's how they work, they generate "thinking" lines to feed back on themselves on top of your prompt. There is no way of separating it.
If you think that confusing message provenance is part of how thinking mode is supposed to work, I don't know what to tell you.
If you think that confusing message provenance is part of how thinking mode is supposed to work, I don't know what to tell you.