Modern Edge-to-Cloud (E2C) systems require fine-grained observability to ensure adaptive behavior and compliance with performance objectives across heterogeneous and dynamic environments. This work introduces an application-level observability framework that integrates developer-driven instrumentation and SLO-aware feedback for autonomous adaptation. By combining OpenTelemetry, Prometheus, K3s, and Chaos Mesh, the framework enables real-time monitoring and adaptive control across the continuum. A video processing use case demonstrates how application-level metrics guide automatic adjustments to maintain target frame rate, latency, and detection accuracy under variable workloads and injected faults. Preliminary results highlight improved scalability, fault tolerance, and responsiveness, providing a practical foundation for adaptive, SLO-compliant E2C applications.