#14475: feat: Add native Azure OpenAI support

## Summary Adds native support for Azure OpenAI models via configuration. ### Changes - **Config:** Added `azure-openai-responses` API type support. - **Core:** Updated model resolution to pass custom `headers` from configuration to the provider, enabling `api-key` header usage required by Azure and other custom gateways. - **Docs:** Added `docs/providers/azure-openai.md` with configuration examples. ### Configuration Example ```json { "models": { "providers": { "azure": { "baseUrl": "...", "api": "azure-openai-responses", "apiKey": "...", "models": [{ "id": "gpt-4", "name": "gpt-4" }] } } } } ``` <!-- greptile_comment --> <h2>Greptile Overview</h2> <h3>Greptile Summary</h3> This PR adds an `azure-openai-responses` model API option to the config schema/types, threads provider-configured HTTP `headers` into inline model resolution, and documents an Azure OpenAI provider configuration. The config/type changes live in `src/config/types.models.ts` and `src/config/zod-schema.core.ts`, while the runtime wiring happens in `src/agents/pi-embedded-runner/model.ts` by carrying `headers` through the resolved `Model` object. Main issue: `azure-openai-responses` is introduced as a selectable API value but there is no corresponding runtime/provider implementation (no code references outside config/docs). Selecting it is therefore expected to mis-route or fail at runtime unless it’s explicitly mapped/handled. Secondary issue: `resolveModel`’s fallback path uses `providers[provider]` without provider-id normalization, unlike the inline-model match path. This can cause configured provider defaults (baseUrl/headers/api) to be skipped when the caller uses an equivalent provider id that normalizes to the same value. <h3>Confidence Score: 2/5</h3> - This PR is not safe to merge as-is due to an unimplemented new API option. - A new `ModelApi` value (`azure-openai-responses`) is added to config/types/docs but has no corresponding runtime/provider handling in the repo (no references outside config/docs). If users select this API, requests are expected to fail or be misrouted at runtime. Additionally, provider config fallback lookup is inconsistent with normalized matching, which can silently drop baseUrl/headers defaults. - src/config/types.models.ts, src/config/zod-schema.core.ts, src/agents/pi-embedded-runner/model.ts <!-- greptile_other_comments_section --> _{(3/5) Reply to the agent's comments like "Can you suggest a fix for this @greptileai?" or ask follow-up questions!} <!-- /greptile_comment -->