Gate finding (C11 r3, Low): the provider-level loop returned the first
entry on the base_url carrying an answer_in_reasoning bool, whatever
provider was live. Two providers: entries on one endpoint (LiteLLM/vLLM
router) leaked one's opt-in to the other, and an earlier sibling's true
overrode the live entry's explicit false (probe: vllm-nemo true + vllm-ds
false on one URL, live custom:vllm-ds -> True).
Match the live custom:<slug> via custom_provider_slug, the helper that
derives that identity from an entry. With no slug match (bare 'custom'),
trust only when every flagged sibling on the endpoint opts in.
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