docs-util: fixes following packages reorg (#9326)

- Typescript config aren't picked up properly anymore since they're moved to `_tsconfig.base.json` in the root. So, we now read the config from the config file.
- Update Typescript version in the `utils` monorepo to match that of the root monorepo

www/utils/packages/scripts/package.json

@@ -23,7 +23,7 @@
     "glob": "^10.3.10",
     "randomcolor": "^0.6.2",
     "ts-node": "^10.9.1",
-    "typescript": "5.5"
+    "typescript": "^5.6.2"
   },
   "devDependencies": {
     "@types/node": "^20.12.10",