refactor: rename web/ to api/ to better reflect its purpose

The web/ folder contains the REST API, WebSocket server, and OAuth
routes — not a web frontend. Renaming to api/ clarifies this distinction
since the actual web frontend lives in panel/.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

api/src/routes/health.routes.ts

@@ -0,0 +1,36 @@
+/**
+ * @fileoverview Health check endpoint for Aurora API.
+ * Provides a simple health status endpoint for monitoring and load balancers.
+ */
+
+import type { RouteContext, RouteModule } from "./types";
+
+/**
+ * Health routes handler.
+ * 
+ * @route GET /api/health
+ * @description Returns server health status with timestamp.
+ * @response 200 - `{ status: "ok", timestamp: number }`
+ * 
+ * @example
+ * // Request
+ * GET /api/health
+ * 
+ * // Response
+ * { "status": "ok", "timestamp": 1707408000000 }
+ */
+async function handler(ctx: RouteContext): Promise<Response | null> {
+    if (ctx.pathname === "/api/health" && ctx.method === "GET") {
+        return Response.json({
+            status: "ok",
+            timestamp: Date.now()
+        });
+    }
+
+    return null;
+}
+
+export const healthRoutes: RouteModule = {
+    name: "health",
+    handler
+};