Set up unit testing infrastructure

- Extract slot generation logic into apps/api/src/lib/slots.ts for testability
- Add 8 unit tests covering slot generation edge cases (overlap, multi-groomer, boundary)
- Add @testing-library/react + jsdom to apps/web; configure vitest with jsdom environment
- Add 4 component tests for App navigation rendering and active-link highlighting
- Remove passWithNoTests: true from both vitest configs; add coverage thresholds

Closes #39

Co-Authored-By: Paperclip <noreply@paperclip.ing>

apps/web/package.json

@@ -18,10 +18,15 @@
     "react-router-dom": "^7.1.2"
   },
   "devDependencies": {
+    "@testing-library/jest-dom": "^6.9.1",
+    "@testing-library/react": "^16.3.2",
+    "@testing-library/user-event": "^14.6.1",
     "@types/react": "^19.0.6",
     "@types/react-dom": "^19.0.3",
     "@vitejs/plugin-react": "^4.3.4",
+    "@vitest/coverage-v8": "^3.2.4",
     "eslint": "^9.18.0",
+    "jsdom": "^26.1.0",
     "typescript": "^5.7.3",
     "typescript-eslint": "^8.20.0",
     "vite": "^6.0.7",