feat(provider): add openai-responses provider_type for the Responses API (#703)

[yogthos]

Closes #703.

A custom provider with provider_type: "openai" always targets /v1/chat/completions. Some OpenAI-compatible endpoints only expose the Responses API (/v1/responses) — e.g. the OAuth proxy in the issue that mirrors what OpenAI itself serves for GPT-5+ — and there was no way to select it.

What

Add a new provider_type: "openai-responses":

"providers": {
  "gpt5-proxy": {
    "provider_type": "openai-responses",
    "model": "gpt-5.6",
    "base_url": "http://127.0.0.1:8639/v1",
    "api_key": "${MY_PROXY_KEY}",
    "allow_insecure": true
  }
}

• Resolves to the OpenAI kind, so every other behavior (default model, env-var fallbacks, base_url/allow_insecure handling, model-family routing) is reused — no ProviderKind explosion.
• Forks only the final client build to the existing ChatGptOpenAI client (openai::Client's Responses adapter) with a non-token CodexHttpClient: a plain api-key bearer against the configured base_url, no OAuth/Codex login. The codex http layer still normalizes the outgoing Responses body (rig 0.37 emits instructions: null + a system item in input), which is the correct shape for any /v1/responses endpoint.
• allow_insecure is honored (the https-only guard only applies to OAuth bearers), so the reporter's http://127.0.0.1 proxy works.
• provider_type: "openai" is unchanged (chat/completions).

Note

Pin a model on the entry. An unset model falls back to the OpenAI default (gpt-4o), which the Codex-default remap (resolve_codex_default, only fires when the model is not explicitly set) would then rewrite — harmless but not what you want against a proxy.

Tests

• parse_provider("openai-responses") → OpenAI kind (both separators, case-insensitive); resolve_provider_info sets the openai_responses flag for it and not for plain openai.
• create_client builds AnyClient::ChatGptOpenAI for openai-responses (and doesn't read the OAuth store), while plain openai still builds AnyClient::OpenAI.
• cargo fmt + cargo clippy --tests clean; provider suite green locally.

Docs: docs/config.md (provider_type table + a "Chat Completions vs Responses API" subsection).

[draxxris]

Thanks. I started on it last night but my subscription hit its limit =V

[yogthos]

ah no worries