Adrien de Peretti 77f37c5f97 Chore(index): Sync logs management (#11522) ...

**What**
- Add index engine sync log information
- Ad `setTimeout(0)` to give breath to the event loop and ensuring not blocking the event loop and allow for other tasks queue execution to happen while syncing

here is an example:
**LOG_LEVEL=info**

![Screenshot 2025-02-19 at 10 09 25](https://github.com/user-attachments/assets/fc74dc32-1bc1-4123-9de3-f37817b7e783)

**LOG_LEVEL=debug**

![Screenshot 2025-02-19 at 10 10 35](https://github.com/user-attachments/assets/222a1ce1-9267-4cb0-9518-dc4c7aa2b6f4)

2025-02-19 11:54:38 +00:00

..

__fixtures__

Chore(index): Sync logs management (#11522)

2025-02-19 11:54:38 +00:00

__tests__

Chore(index): Sync logs management (#11522)

2025-02-19 11:54:38 +00:00