test: component tests with jsdom and Testing Library

First tests cover the library search debounce (fails on the old looping
version), the Pile of Shame states and the backlog save body. jsdom is
enabled per test file, so the plain util tests stay in the node environment.

package.json

@@ -29,8 +29,11 @@
     "zod": "^3.25.76"
   },
   "devDependencies": {
+    "@testing-library/dom": "^10.4.2",
+    "@testing-library/react": "^16.3.3",
     "@vitejs/plugin-react": "^6.1.1",
     "autoprefixer": "~10.6.1",
+    "jsdom": "^30.1.1",
     "postcss": "~8.5.28",
     "tailwindcss": "~4.3.3",
     "tw-animate-css": "^1.4.0",