Support Azure AI Foundry OpenAI models via the Responses API (Fixes #47)

[Izzetee]

What

Adds support for Azure AI Foundry OpenAI models served through the OpenAI Responses API (/openai/v1/responses).

Fixes #47.

Why

Azure AI Foundry now serves OpenAI deployments (e.g. gpt-5.x) via the Responses API, which replaces the Chat Completions messages field with input and returns an output array instead of choices. PiPiMink only spoke Chat Completions, so tagging/chat/routing/benchmarking failed with:

HTTP 400: Unsupported parameter: 'messages'. In the Responses API, this parameter has moved to 'input'.
tag: error tagging model gpt-5.6-terra (az-foundry): missing or empty choices in response

…and the model was auto-disabled.

How

Backend

• New provider type openai-responses, plus auto-detection when a chat_path targets /responses (so existing path-only overrides work and future migrations keep working).
• New ProviderConfig.UsesResponsesAPI() and ResponsesURL() helpers.
• New internal/llm/responses.go: request builder (input) and a robust response parser (output → message → output_text, with error and incomplete_details handling).
• Wired into tagging, chat, model selection, and the benchmark judge.
• temperature and max_output_tokens are omitted by default so reasoning models (o-series, gpt-5.x) are not rejected and manage their own output budget.

Frontend

• openai-responses added to the type union, the provider and per-model type selectors, a provider-list badge, and a chat-path hint.

Docs & config

• README, SETUP (new endpoint pattern + diagram/table/example), CHANGELOG, AGENTS, copilot-instructions, providers.example.json, .env.example.

Testing

• go build ./..., go test -short ./... — all pass.
• New unit tests: UsesResponsesAPI/ResponsesURL/ForModel override; buildResponsesInput/buildResponsesPayload/extractResponsesContent; an end-to-end chat test asserting the /responses endpoint is hit and the body uses input (not messages).
• Frontend: tsc --noEmit, vitest run (22 passed), npm run build — all pass.
• markdownlint-cli2 — 0 errors.

How to configure

{
  "name": "gpt-5",
  "type": "openai-responses",
  "chat_path": "/openai/v1/responses",
  "api_key_env": "AZURE_FOUNDRY_GPT5_API_KEY"
}