feat(gateway): support hosted Responses API with Flux billing

Goal

Add Responses API to AIRI's authenticated gateway and settle hosted generation through the existing Flux policy.

Scope

• Add stateless POST /api/v1/openai/responses with native JSON and SSE forwarding.
• Select only upstreams that explicitly declare Responses support.
• Reuse authentication, rate limits, aliases, tracing, and Flux debit transactions.
• Charge completed requests from their input/output usage. Do not charge failed, incomplete, cancelled, or truncated streams.
• Enable Responses for the official provider after the client adapter is available.

Acceptance criteria

• Gateway and router regressions cover success, error, cancellation, usage, and protocol selection.
• Unsupported upstreams do not receive Responses requests.
• The stateless endpoint rejects provider-side conversation references and hosted tools with separate charges.
• The official provider retains authenticated credentials.
• Live gateway and Flux behavior are checked before release.

The BYOK client work in #2477 does not depend on this issue. No live configuration or deployment is included. Realtime sessions and a separate search service are outside this issue.