Recently, the need for unified orchestration frameworks that can manage extremely heterogeneous, distributed, and resource-constrained environments has arisen due to the rapid development of cloud, edge, and IoT computing. Kubernetes and other traditional cloud-native orchestration systems are not built to facilitate autonomous, decentralized decision-making across the computing continuum or to seamlessly integrate non-container-native devices. This paper presents the Distributed Adaptive Cloud Continuum Architecture (DACCA), a Kubernetes-native architecture that extends orchestration beyond the data center to encompass edge and Internet of Things infrastructures. Decentralized self-awareness and swarm formation are supported for adaptive and resilient operation, a resource and application abstraction layer is established for uniform resource representation, and a Distributed and Adaptive Resource Optimization (DARO) framework based on multi-agent reinforcement learning is integrated for intelligent scheduling in the proposed architecture. Verifiable identity, access control, and tamper-proof data exchange across heterogeneous domains are further guaranteed by a distributed-ledger-technology-based zero-trust security framework. When combined, these elements enable completely autonomous workload orchestration with enhanced interoperability, scalability, and trust. Thus, the proposed architecture enables self-managing and context-aware orchestration systems that support next-generation AI-driven distributed applications across the entire computing continuum.