Task scheduling and offloading are essential disciplines in edge and fog computing, enabling the distribution of workloads, encapsulated as tasks, across heterogeneous nodes. This distribution is typically based on properties and requirements and can have various objectives, such as optimizing quality of service and experience, including response time, energy consumption, or costs. Many advanced orchestration techniques exist to achieve a proper workload distribution. However, they are primarily evaluated through simulations. This work aims to close this research gap and addresses real-world task scheduling and offloading evaluations, which are also explicitly desired by authors of those advanced orchestration techniques. We conceptually integrated the necessary capabilities to perform task scheduling and offloading into our holistic cloud-edge orchestration management life cycle. Additionally, we implemented these capabilities within our orchestration platform, PULCEO, and conducted typical evaluations. Our approach shows that our platform can perform task scheduling and offloading with minimal overhead on the overall orchestration performance. At this, we can fully maintain the benefits of holistic and decoupled orchestration efforts.