Modern applications increasingly span across cloud, fog, and edge environments, demanding orchestration systems that can adapt to diverse deployment contexts while meeting Quality-of-Service (QoS) requirements. Standard Kubernetes schedulers do not account for user-defined objectives such as energy efficiency, cost optimization, and global performance, often leaving operators to make manual, cluster-by-cluster placement decisions. To address this need, we present QONNECT, a vendor-agnostic orchestration framework that enables declarative, QoS-driven application deployment across heterogeneous Kubernetes and K3s clusters. QONNECT introduces a distributed architecture composed of a central Knowledge Base, Raft-replicated Resource Lead Agents, and lightweight Resource Agents in each cluster. Through a minimal YAML-based interface, users specify high-level QoS goals, which the system translates into concrete placement and migration actions. Our implementation is evaluated on a federated testbed of up to nine cloud-fog-edge clusters using the Istio Bookinfo microservice application. The system demonstrates dynamic, policy-driven microservice placement, automated failover, QoS-compliant rescheduling, and leader re-election after node failure, all without manual intervention. By bridging the gap between declarative deployment models and operational QoS goals, QONNECT transforms the cloud-edge continuum into a unified, self-optimizing platform.