Add tests for URL fragment routing behavior with order-independent window mocking

- Add tests for hash routing based on server capabilities priority
  - Test that no hash is set when disconnected
  - Add e2e test verifying startup has no hash fragment
  - Use Jest module mocking for useConnection hook states

🤖 Generated with [Claude Code](https://claude.ai/code)

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

client/e2e/startup-state.spec.ts

@@ -0,0 +1,16 @@
+import { test, expect } from "@playwright/test";
+
+// Adjust the URL if your dev server runs on a different port
+const APP_URL = "http://localhost:6274/";
+
+test.describe("Startup State", () => {
+  test("should not navigate to a tab when Inspector first opens", async ({
+    page,
+  }) => {
+    await page.goto(APP_URL);
+
+    // Check that there is no hash fragment in the URL
+    const url = page.url();
+    expect(url).not.toContain("#");
+  });
+});