We're using Zephyr Enterprise 6.1. I've been using the documentation at https://zephyr61.docs.apiary.io/
From my experience with APIs, there is usually a GET for an endpoint (e.g., testcases) that returns all of that type of endpoint. I don't see that in the documentation. I have accidentally found API calls that were not in that documentation and so I'm hoping that getting all the testcases is available but just not documented.
What you can use is make use of the advance search ZQL and put it forward to get the results you are looking frim the API. You can also use the same filters from the UI's network calls.
Please note that it is good practice to check the network call for referring to the API's however the internal APIS which are not listed in the APIry are subjected to change in future.