API economy is driving the digital transformation of business applications across the hybrid Cloud and edge environments. For such transformations to succeed, end-to-end testing of the application API composition is required. Testing of API compositions, even in centralized Cloud environments, is challenging as it requires coverage of functional as well as reliability requirements. The combinatorial space of scenarios is huge, e.g., API input parameters, order of API execution, and network faults. Hybrid Cloud and edge environments exacerbate the challenge of API testing due to the need to coordinate test execution across dynamic wide-area networks, possibly across network boundaries. To handle this challenge, we envision a test framework named Distributed Software Test Kit (DSTK). The DSTK leverages Combinatorial Test Design (CTD) to cover the functional requirements and then automatically covers the reliability requirements via under-the-hood closed loop between test execution feedback and AI based search algorithms. In each iteration of the closed loop, the search algorithms generate more reliability test scenarios to be executed next. Specifically, five kinds of reliability tests are envisioned: out-of-order execution of APIs, network delays and faults, API performance and throughput, changes in API call graph patterns, and changes in application topology.