refactor: make workspaces fully self-contained

Removed shared dependencies from root package.json. Each workspace now
manages its own dependencies independently.

- Removed prettier from root devDependencies
- Removed prettier scripts from root (available in web-app workspace)
- Root package.json now only manages workspace configuration

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

package-lock.json

@@ -11,9 +11,6 @@
         "web-app",
         "housekeeping"
       ],
-      "devDependencies": {
-        "prettier": "^3.0.3"
-      },
       "engines": {
         "node": ">=18.17.0"
       }

package.json

@@ -9,12 +9,7 @@
   "scripts": {
     "dev": "npm run dev --workspace=web-app",
     "build": "npm run build --workspace=web-app",
-    "start": "npm run start --workspace=web-app",
-    "prettier": "prettier --write --ignore-unknown .",
-    "prettier:check": "prettier --check --ignore-unknown ."
-  },
-  "devDependencies": {
-    "prettier": "^3.0.3"
+    "start": "npm run start --workspace=web-app"
   },
   "engines": {
     "node": ">=18.17.0"