Add Vitest test infrastructure, api.ts unit tests, and CI pipeline

Summary

• Set up Vitest + React Testing Library (jsdom environment, jest-dom matchers, coverage via v8) as the project's test infrastructure, with a smoke test on Badge proving the pipeline end to end.
• Added a full unit test suite for the mock API layer (src/lib/api.ts), covering all 12 exported functions, their audit-log side effects, sort ordering, and not-found paths — using fake timers to flush the artificial network latency deterministically instead of waiting on real time.
• Added a GitHub Actions CI workflow that runs lint, typecheck/build, and tests on every push to main and every PR, scoped to client/.

Details

• vite.config.ts extended via vitest/config's defineConfig with a test block (jsdom, setupFiles, v8 coverage reporters)
• src/test/setup.ts wires in @testing-library/jest-dom
• New scripts: npm test, npm run test:watch, npm run test:coverage
• src/lib/api.test.ts resets the module registry per test (the mock API holds mutable module-level state) and uses vi.advanceTimersByTimeAsync to flush delays
• .github/workflows/ci.yml: Node 22, npm ci → npm run lint → npm run build → npm test
• client/README.md documents the test commands; coverage/ added to .gitignore

Test plan

• npm run lint — clean (only 2 pre-existing, unrelated fast-refresh warnings)
• npm run build — type-checks and builds clean
• npm test — 20/20 tests passing
• npm run test:coverage — coverage report generates correctly
• CI workflow YAML validated (js-yaml parse)

Closes #3
Closes #4
Closes #5