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.

package.json

@@ -33,9 +33,5 @@
 	"engines": {
 		"node": ">=20.0.0"
 	},
-	"version": "0.0.2",
-	"dependencies": {
-		"@mariozechner/jailjs": "^0.1.1",
-		"@mariozechner/mini-lit": "^0.1.8"
-	}
+	"version": "0.0.2"
 }