-6th generation cellular networks are foreseen to enable various mission-critical use cases, not only by means of communications, but also by the integration of sensing capabilities, referred to as joint communications and sensing. However, both communications and sensing are sensitive to interfering signals that can degrade communication or sensing performance. To ensure spectrum integrity in non-public networks (NPNs), we propose leveraging a radio environment digital twin (DT) to compare the channel frequency response (CFR) of the real-world wireless channel with that of the digital twin, referred to as digital twin channel (DTC). Significant deviations between the two may indicate spectrum anomalies, i.e., any kind of interfering signal. In an evaluation on measurement data collected from a workshop environment, the proposed approach achieves a missed detection rate below 0.1% for a tolerated false positive rate (FPR) of 1%. Moreover, non-smooth regions in the CFR can serve as an additional indicator of spectrum anomalies. Using the magnitude of the forward difference as a measure of non-smoothness and combine the two approaches, the missed detection rate can be further reduced to 4 · 10^-5 while maintaining a constant FPR. Thus, this paper demonstrates that integrating contextual awareness, enabled by DT, facilitates high-fidelity spectrum anomaly detection, a critical capability for building resilient future NPN.