> And how is the confidence score any different than the softmaxed token probabilities you get out of running every llm?

You're asking me how a structured output which assigns probabilities to classifications of the input text is different than the next-token weights which are calculated while generating that output?

One is internal (token prob), one is output generated by that internal mechanism e.g.,

    "{ next_state: { "evade": 0.84, "land": 0.10, "search": 0.01"...}}"