The Computing Continuum (CC) is an emerging Internet-based computing paradigm that spans from local Internet of Things sensors and constrained edge devices to large-scale cloud data centers. Its goal is to orchestrate a vast array of diverse and distributed computing resources to support the next generation of Internet-based applications. However, the distributed, heterogeneous, and dynamic nature of CC platforms demands distributed intelligence for adaptive and resilient service management. This article introduces a distributed stream processing pipeline as a CC use case, where each service is managed by an Active Inference (AIF) agent. These agents collaborate to fulfill service needs specified by SLOiDs, a term we introduce to denote Service Level Objectives that are aware of its deployed devices, meaning that non-functional requirements must consider the characteristics of the hosting device. We demonstrate how AIF agents can be modeled and deployed alongside distributed services to manage them autonomously. Our experiments show that AIF agents achieve over 90% SLOiD fulfillment when using tested transition models, and around 80% when learning the models during deployment. We compare their performance to a multi-agent reinforcement learning algorithm, finding that while both approaches yield similar results, MARL requires extensive training, whereas AIF agents can operate effectively from the start. Additionally, we evaluate the behavior of AIF agents in offloading scenarios, observing a strong capacity for adaptation. Finally, we outline key research directions to advance AIF integration in CC platforms.