DX: Set up basic testing infrastructure (Vitest + @nuxt/test-utils)

[TusharW4ni]

Context / Problem

Currently, there are no test libraries installed or configured. For a university template, it is important to encourage testing (like TDD) early. Without the infrastructure pre-configured, students are unlikely to write tests.

Proposed Solution

Add @nuxt/test-utils and vitest to establish a baseline testing setup.

Implementation Details

1. Install the testing dependencies:

   pnpm add -D vitest @vue/test-utils @nuxt/test-utils

2. Add a vitest.config.ts if required by the Nuxt testing docs.
3. Add a basic example test in a tests/ directory (e.g., tests/auth.test.ts or an example component test) to serve as a reference.
4. Add a test script to package.json: "test": "vitest".

Acceptance Criteria

• Vitest and Nuxt Test Utils are installed and configured.
• pnpm run test executes successfully.
• At least one example test exists to guide students.