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.impl.ts

@@ -111,6 +111,11 @@ export type GatewayServerOptions = {
    * Default: config `gateway.http.endpoints.chatCompletions.enabled` (or false when absent).
    */
   openAiChatCompletionsEnabled?: boolean;
+  /**
+   * If false, do not serve `POST /v1/responses` (OpenResponses API).
+   * Default: config `gateway.http.endpoints.responses.enabled` (or false when absent).
+   */
+  openResponsesEnabled?: boolean;
   /**
    * Override gateway auth configuration (merges with config).
    */
@@ -205,6 +210,7 @@ export async function startGatewayServer(
     host: opts.host,
     controlUiEnabled: opts.controlUiEnabled,
     openAiChatCompletionsEnabled: opts.openAiChatCompletionsEnabled,
+    openResponsesEnabled: opts.openResponsesEnabled,
     auth: opts.auth,
     tailscale: opts.tailscale,
   });
@@ -212,6 +218,7 @@ export async function startGatewayServer(
     bindHost,
     controlUiEnabled,
     openAiChatCompletionsEnabled,
+    openResponsesEnabled,
     controlUiBasePath,
     resolvedAuth,
     tailscaleConfig,
@@ -250,6 +257,7 @@ export async function startGatewayServer(
     controlUiEnabled,
     controlUiBasePath,
     openAiChatCompletionsEnabled,
+    openResponsesEnabled,
     resolvedAuth,
     gatewayTls,
     hooksConfig: () => hooksConfig,