* fix(cost): bill a provider reported usage.cost on every path unless the deployment is priced
* test(integration): a reported cost is attributed to output in the gateway parity cases
* fix(cost): skip a chat usage.cost that already holds litellm's stamped bill and Responses API objects
* fix(cost): record litellm's bill on the Responses terminal event so a later pricing pass does not read it as the upstream's charge
* fix(cost): mark usage.cost litellm wrote as its own bill and keep a breakdown for a reported cost
* fix(cost): keep the token breakdown when a header reported cost repeats an already priced bill
* fix(cost): read the stored breakdown total through the logging object's typed field
* refactor(cost): name the providers billed from their own usage fields for what they are
* fix(cost): keep the upstream's usage.cost beside litellm's bill and stamp a zero operator price on the stream frame
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Co-authored-by: devin-ai-integration[bot] <158243242+devin-ai-integration[bot]@users.noreply.github.com>