I want to get a list of items which customers left in their shopping cart (abandoned cart) from my store using the Magento API
I can't find any API call in the below documentation, to get such list
Check below link,here all api is defined to get and post cart item data:
For Quote API-> there is a list of api that you can use
GET /V1/carts/:cartId * GET /V1/carts/search POST /V1/carts/ POST /V1/customers/:customerId/carts PUT /V1/carts/:cartId POST /V1/carts/mine GET /V1/carts/mine * PUT /V1/carts/mine PUT /V1/carts/mine/order GET /V1/guest-carts/:cartId POST /V1/guest-carts PUT /V1/guest-carts/:cartId PUT /V1/guest-carts/:cartId/order .....
You can get all type of cart items(for logged in or guest customers) by using above api.
Also you can check link,which will be useful for you. Let me know if you need any help.