Add health check API route

Expose GET /health that returns JSON {status, timestamp}. Returns 200 on success
and 500 on error. Disable prerender for the endpoint.

src/pages/health.ts

@@ -0,0 +1,24 @@
+import type { APIRoute } from "astro";
+export const prerender = false;
+
+export const GET: APIRoute = async () => {
+  try {
+    return new Response(
+      JSON.stringify({
+        status: "pass",
+        timestamp: new Date().toISOString(),
+      }),
+      {
+        status: 200,
+      },
+    );
+  } catch {
+    return new Response(
+      JSON.stringify({
+        status: "fail",
+        timestamp: new Date().toISOString(),
+      }),
+      { status: 500 },
+    );
+  }
+};