Entries out of order when searching in the tool picker

<img width="699" alt="Image" src="https://github.com/user-attachments/assets/37c1658d-bb87-414c-8971-f93c79086cf7" />

We should try to keep the parent/child ordering

<img width="636" alt="Image" src="https://github.com/user-attachments/assets/b47cce66-4680-4ea3-83be-6d6ac5c7d06e" />