In the Industrial Internet of Things (IIoT), Time-Sensitive Networking (TSN) is a promising field network of implementing application functions across distributed devices. For a TSN-engaged IIoT system, co-scheduling task execution and TSN transmission is crucial to guarantee the chain execution of application tasks. However, the generalization ability of co-scheduling across varying scenarios is hindered in existing works, which lack characterization for resource conflicts arising from semantic relations among tasks, traffic, and the underlying topology. To address this, we propose a heterogeneous graph neural network (HGNN)-based co-scheduling method featuring explicit conflict characterization. We design a semantic-aware encoder within the HGNN, which aggregates heterogeneous component features through designated graph paths to capture their semantic relations. An agent then extracts conflict patterns from this encoding, and decodes conflict-free scheduling decisions on offloading, task priority assignment, and traffic offset design. To enhance generalization ability in unseen scenarios, the conflict extraction ability and the inductive encoding ability are refined through deep reinforcement learning feedback. Experiments demonstrate that our method achieves 12% higher schedulability and 20% lower task chain delay, and maintains its performance in unseen topologies and task scenarios.