Two open atoms of #83390 (DeepSeek "This response_format type is unavailable now"):
* `_call_fallback_candidate_sync/_async` only special-cased auth errors, so when the primary
aux provider failed (timeout, rate limit, payment) and the fallback landed on a provider that
rejects `json_schema`, the 400 re-raised and the whole task died — the primary-path rung from
#89589 never applied there. Both fallback paths now retry once without `response_format`.
* Every structured aux call (titles, kanban decomposer, goal judge, plugin structured calls)
paid a guaranteed-fail request on providers that lack `json_schema` before the retry. A
provider profile can now declare `unsupported_response_formats` (DeepSeek: json_schema, per
https://api-docs.deepseek.com/guides/json_mode) and the recovery ladder remembers any route
that rejected a type once (host:port scoped), so `_build_call_kwargs` — shared by the primary
and fallback paths — omits the field before the first request. Dropping rather than
downgrading to json_object matches the end state the retry already produced; json_object
needs a JSON-mentioning prompt and some relays return empty content under it.
New logic lives in agent/auxiliary_structured_output.py; the facade only gains the fallback rung
next to the predicate it uses. tests/agent/conftest.py resets the process-level memo per test.
Fixes#83390, #105191. Closes duplicates #84976, #88830, #102849, #113064.
Co-authored-by: Legion-is-life <Legion-is-life@users.noreply.github.com>
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