Add structured outputs documentation for LLM Gateway

[devin-ai-integration]

Summary

Adds documentation for the structured outputs feature in LLM Gateway, which allows constraining model responses to follow a specific JSON schema using the response_format parameter.

Documentation page (fern/pages/07-llm-gateway/structured-outputs.mdx):

• Overview explaining the feature
• Code examples in Python, JavaScript, and cURL (based on the provided curl example)
• Example response showing the JSON output format
• Supported models table (OpenAI GPT-4.1/GPT-5.x and Gemini supported; Claude and gpt-oss not supported)
• API reference for the response_format and json_schema parameters
• Best practices and error handling guidance

OpenAPI spec updates (llm-gateway.yml):

• Added response_format parameter to LLMGatewayRequest schema
• Added ResponseFormat and JsonSchemaConfig schema definitions
• Added structured output example in request examples

Updates since last revision

• Added response_format parameter to the LLM Gateway OpenAPI specification so it now appears in the API reference
• Added schema definitions for ResponseFormat (with type and json_schema properties) and JsonSchemaConfig (with name, schema, and strict properties)
• Added a structured output example to the API request examples

Review & Testing Checklist for Human

• Verify OpenAPI schema accuracy: Confirm the ResponseFormat and JsonSchemaConfig schemas match the actual API implementation (especially the enum: [json_schema] for type - are there other valid values?)
• Test the API reference: After deployment, verify response_format appears correctly in the API reference at /docs/api-reference/llm-gateway/create-chat-completion
• Verify supported models: OpenAI (GPT-4.1, GPT-5.x) = yes, Gemini = yes, gpt-oss = no, Claude = no
• Confirm hidden status: Page is hidden: true (matches other LLM Gateway pages, but verify this is intentional)

Recommended test plan:

1. Run the cURL example from the docs against the LLM Gateway to verify structured outputs work as documented
2. Check the preview deployment to confirm the response_format parameter appears in the API reference with correct schema details

Notes

CI failures are pre-existing issues in transcripts.yml (unrelated to this PR). The [docs] validation passed.

Requested by Dan Ince via Slack #ask-api-docs

Link to Devin run: https://app.devin.ai/sessions/4424438ef4014e0e886900b5303e6a6b

[devin-ai-integration]

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