That’s how typical classification and detection CNNs work. Class and confidence value along with bounding box for detection CNNs.
CNNs and LLMs are not that different. You can train an LLM architecture to do the same thing that CNNs do with a few modifications, see Vision Transformers.
But the second-order 'confidence as a symbolic sequence in the stream' is only (very) vaguely tied to this. Numbers-as-symbols are of different kind to numbers-as-next-token-probabilities. I don't doubt there is _some_ relation, but it's too much inferential distance away and thus worth almost nothing.
With that said, nothing really stops you from finetuning an LLM to produce accurately calibrated confidence values as symbols in the token stream. But you have to actually do that, it doesn't come for free by default.
If you give the model the image and a prior prediction, what can it tell you? Asking for it to produce a 1-10 figure in the same token stream as the actual task seems like a flawed strategy.