Get all the data till nth level in content delivery Api

I have attached an image that shows my carousel items.
Currently, I am using the following URL:

/umbraco/delivery/api/v2/content/item/carousel?expand=properties[$all]&fields=properties[$all]

This URL allows me to retrieve the carousel details, but it does not return the carousel item details.
Could someone please help me with the correct URL to fetch the carousel items as well?

Kind regards,
Aadarsh Dubey