feat(api): Hono backend skeleton with /health endpoint and test

apps/api/test/health.test.ts

@@ -0,0 +1,11 @@
+import { describe, it, expect } from 'vitest';
+import { createApp } from '../src/app';
+
+describe('GET /health', () => {
+  it('returns { status: "ok" }', async () => {
+    const app = createApp();
+    const res = await app.request('/health');
+    expect(res.status).toBe(200);
+    expect(await res.json()).toEqual({ status: 'ok' });
+  });
+});

apps/api/test/setup.ts

@@ -0,0 +1,2 @@
+// Placeholder until Task 3 adds DB migration to the test setup.
+export {};