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/config/types.gateway.ts

@@ -105,8 +105,17 @@ export type GatewayHttpChatCompletionsConfig = {
   enabled?: boolean;
 };
 
+export type GatewayHttpResponsesConfig = {
+  /**
+   * If false, the Gateway will not serve `POST /v1/responses` (OpenResponses API).
+   * Default: false when absent.
+   */
+  enabled?: boolean;
+};
+
 export type GatewayHttpEndpointsConfig = {
   chatCompletions?: GatewayHttpChatCompletionsConfig;
+  responses?: GatewayHttpResponsesConfig;
 };
 
 export type GatewayHttpConfig = {

src/config/zod-schema.ts

@@ -299,6 +299,12 @@ export const ClawdbotSchema = z
                   })
                   .strict()
                   .optional(),
+                responses: z
+                  .object({
+                    enabled: z.boolean().optional(),
+                  })
+                  .strict()
+                  .optional(),
               })
               .strict()
               .optional(),