feat(gateway): add OpenResponses /v1/responses endpoint

Add a new `/v1/responses` endpoint implementing the OpenResponses API
standard for agentic workflows. This provides:

- Item-based input (messages, function_call_output, reasoning)
- Semantic streaming events (response.created, response.output_text.delta,
  response.completed, etc.)
- Full SSE event support with both event: and data: lines
- Configuration via gateway.http.endpoints.responses.enabled

The endpoint is disabled by default and can be enabled independently
from the existing Chat Completions endpoint.

Phase 1 implementation supports:
- String or ItemParam[] input
- system/developer/user/assistant message roles
- function_call_output items
- instructions parameter
- Agent routing via headers or model parameter
- Session key management

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

src/gateway/server-http.ts

@@ -26,6 +26,7 @@ import {
 } from "./hooks.js";
 import { applyHookMappings } from "./hooks-mapping.js";
 import { handleOpenAiHttpRequest } from "./openai-http.js";
+import { handleOpenResponsesHttpRequest } from "./openresponses-http.js";
 
 type SubsystemLogger = ReturnType<typeof createSubsystemLogger>;
 
@@ -192,6 +193,7 @@ export function createGatewayHttpServer(opts: {
   controlUiEnabled: boolean;
   controlUiBasePath: string;
   openAiChatCompletionsEnabled: boolean;
+  openResponsesEnabled: boolean;
   handleHooksRequest: HooksRequestHandler;
   handlePluginRequest?: HooksRequestHandler;
   resolvedAuth: import("./auth.js").ResolvedGatewayAuth;
@@ -202,6 +204,7 @@ export function createGatewayHttpServer(opts: {
     controlUiEnabled,
     controlUiBasePath,
     openAiChatCompletionsEnabled,
+    openResponsesEnabled,
     handleHooksRequest,
     handlePluginRequest,
     resolvedAuth,
@@ -222,6 +225,9 @@ export function createGatewayHttpServer(opts: {
       if (await handleHooksRequest(req, res)) return;
       if (await handleSlackHttpRequest(req, res)) return;
       if (handlePluginRequest && (await handlePluginRequest(req, res))) return;
+      if (openResponsesEnabled) {
+        if (await handleOpenResponsesHttpRequest(req, res, { auth: resolvedAuth })) return;
+      }
       if (openAiChatCompletionsEnabled) {
         if (await handleOpenAiHttpRequest(req, res, { auth: resolvedAuth })) return;
       }