Adds Vitest and Playwright testing setup with sample tests

Introduces a unified testing setup using Vitest for unit tests
and Playwright for E2E tests. Updates dependencies, adds sample
unit and E2E tests, documents test workflow, and codifies
testing and code standards in project guidelines.

Enables fast, automated test runs and improves code reliability
through enforced standards.

README.md

@@ -104,6 +104,24 @@ To run locally:
    ```
 4. Visit [http://localhost:3000](http://localhost:3000) and unleash the fire.
 
+### Running Tests 🧪
+
+We use **Vitest** for unit testing and **Playwright** for end-to-end (E2E) testing.
+
+**Unit Tests:**
+```bash
+pnpm test
+```
+
+**E2E Tests:**
+```bash
+# First install browsers (only needed once)
+pnpm exec playwright install
+
+# Run tests
+pnpm test:e2e
+```
+
 ---
 
 ## ✏️ Inputs & Variables