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-runtime-config.ts

@@ -17,6 +17,7 @@ export type GatewayRuntimeConfig = {
   bindHost: string;
   controlUiEnabled: boolean;
   openAiChatCompletionsEnabled: boolean;
+  openResponsesEnabled: boolean;
   controlUiBasePath: string;
   resolvedAuth: ResolvedGatewayAuth;
   authMode: ResolvedGatewayAuth["mode"];
@@ -33,6 +34,7 @@ export async function resolveGatewayRuntimeConfig(params: {
   host?: string;
   controlUiEnabled?: boolean;
   openAiChatCompletionsEnabled?: boolean;
+  openResponsesEnabled?: boolean;
   auth?: GatewayAuthConfig;
   tailscale?: GatewayTailscaleConfig;
 }): Promise<GatewayRuntimeConfig> {
@@ -45,6 +47,8 @@ export async function resolveGatewayRuntimeConfig(params: {
     params.openAiChatCompletionsEnabled ??
     params.cfg.gateway?.http?.endpoints?.chatCompletions?.enabled ??
     false;
+  const openResponsesEnabled =
+    params.openResponsesEnabled ?? params.cfg.gateway?.http?.endpoints?.responses?.enabled ?? false;
   const controlUiBasePath = normalizeControlUiBasePath(params.cfg.gateway?.controlUi?.basePath);
   const authBase = params.cfg.gateway?.auth ?? {};
   const authOverrides = params.auth ?? {};
@@ -88,6 +92,7 @@ export async function resolveGatewayRuntimeConfig(params: {
     bindHost,
     controlUiEnabled,
     openAiChatCompletionsEnabled,
+    openResponsesEnabled,
     controlUiBasePath,
     resolvedAuth,
     authMode,