Driven by the new generation of information technology, modern manufacturing is shifting from traditional rigid production to flexible, customized models. This transformation imposes higher demands on systems' dynamic adaptability and real-time responsiveness. The emergence of Edge Computing (EC) and the Age of Information (AoI) offers promising solutions to these challenges. Significant progress has been made in areas such as edge resource allocation and information update strategies, contributing to enhanced system responsiveness. However, most existing studies assume task independence, which limits their applicability in complex scenarios (such as high-end manufacturing), where task dependency is dynamic and ubiquitous. In addition, ensuring end-to-end integration of sensing, transmission, computation, and control (STCC) remains a major challenge. To address this gap, this study proposes a collaborative framework focusing on sensing, transmission, computation, and control (STCC), centering around task chains. For the first time, it introduces and defines the Dependency-Aware Age of Information (DAoI) metric to quantify inter-task dependencies and the effects of delay propagation, thereby enabling a more accurate assessment of data timeliness. Additionally, an optimal controller using the Linear Quadratic Regulator (LQR) is designed. Our model optimizes control performance and energy consumption through a Markov Decision Process (MDP). The proposed Dependency-Aware Heterogeneous Task and Resource Co-scheduling (MAPPO-DHTCO) algorithm efficiently manages task dependencies and resource allocation. Experimental results show that this method has significantly improved performance compared to the benchmark method.