Fix Lit dependency duplication and update mini-lit to 0.2.0

- Move lit from dependencies to peerDependencies in web-ui to prevent multiple Lit instances being loaded
- Update mini-lit from 0.1.8/0.1.10 to 0.2.0 in root package.json and web-ui/package.json
- Install @tailwindcss/vite in web-ui/example
- Run biome formatting fixes across codebase

This resolves HMR custom element re-registration errors caused by duplicate Lit registries.

packages/web-ui/example/package.json

@@ -9,7 +9,7 @@
     "check": "tsc --noEmit"
   },
   "dependencies": {
-    "@mariozechner/mini-lit": "^0.1.7",
+    "@mariozechner/mini-lit": "^0.2.0",
     "@mariozechner/pi-ai": "file:../../ai",
     "@mariozechner/pi-web-ui": "file:../",
     "@tailwindcss/vite": "^4.1.17",