Return a Runnable that produces structured output.
Parallel's research models (lite, base, core) accept the
OpenAI response_format parameter with a JSON schema. The speed
model silently ignores it; this method raises if you try to use it
on a non-supporting model so the failure is loud.
"json_schema" (default) for strict-typed output, or
"json_mode" to ask the model for any valid JSON object.
"function_calling" is accepted for cross-provider
compatibility and is routed to "json_schema" since
Parallel's chat API does not support tool calling.
If True, return {"raw": AIMessage, "parsed": ..., "parsing_error": ...} instead of just the parsed value.
Forwarded to the API's response_format JSON schema.
Defaults to True for pydantic schemas, None for raw dicts.
Reserved for forward compatibility; unused.
