Integrated sensing and communication (ISAC) networks can serve compatible requests through shared sensing sessions, but consolidation couples admission, reuse, profile selection, sensing service-level agreements (SLAs), communication quality of service (QoS), and future commitments. We formulate this problem as a constrained Markov decision process and propose Common-Trace Factorized Constrained Proximal Policy Optimization (CT-PPO). During training, stochastic policy replicas share the same primitive workload trace; leave-one-out discounted Monte Carlo return contrasts provide reward credit to applicable actor factors, while constraint credit remains factor/prefix-specific. Across five training seeds and matched workloads, CT-PPO achieves the highest mean macro return, exceeding matched Joint-Credit PPO (JC-PPO) by 0.934 (95% confidence interval [0.702, 1.164]) and SLA-Aware Greedy by 1.847; versus JC-PPO, it reduces sensing-resource cost by 6.277 and raises accepted requests per created session by 0.0806. A four-way ablation shows that the factorized surrogate alone yields no detectable macro-return gain, whereas adding common-trace reward credit produces the dominant improvement. Without retraining, CT-PPO retains a return advantage at low, nominal, and high arrival loads, with the strongest gain under clustered arrivals. Deployment uses public observations and hard masks; CT-PPO's extra parameters are training-side, its actor footprint matches JC-PPO, and actor-only CPU latency is effectively unchanged.

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