feat: migrate from npm to Bun

- Install Bun via mise
- Update package.json scripts to use Bun
- Migrate unit tests from Vitest to Bun test runner
- Migrate component tests from Vitest to Bun test runner
- Configure Bun with DOM environment for React Testing Library
- Keep Playwright for E2E tests (as planned)
- 93/100 tests passing (7 flaky tests when running all together, pass individually)

src/__tests__/unit/id-validation.test.ts

@@ -4,7 +4,7 @@
  * Tests for ID parsing and validation in API routes and pages
  */
 
-import { describe, test, expect } from 'vitest';
+import { describe, test, expect } from 'bun:test';
 
 describe('ID Validation', () => {
   describe('parseInt with validation', () => {