In this paper, we consider resource allocation for a collaborative integrated sensing and communication (ISAC) scenario, in which distributed smart devices can be scheduled to perform sensing and transmit their sensing features to a fusion center. The fusion center aims to perform classification tasks on the environment based on received features. A scalable networksensing framework is proposed to balance the performance of the sensing service with that of the classical enhanced Mobile Broadband (eMBB) service. We adopt a tractable theoretical metric, the discriminant gain, as a proxy for the classification goal. We formulate cross-layer optimization problems to maximize discriminant gain under constraints on energy consumption and eMBB communication quality for the independent and joint scheduling policies. The joint scheduling policy has considerably higher complexity than the independent scheduling policy, in exchange for better collaborative sensing performance. A simplified gain model is proposed to reduce the complexity and practicality of the joint scheduling policy. Both policies are obtained via successive convex approximation and parametric convex optimization. Extensive experiments are conducted to verify the goal-oriented framework and the two policies. It is demonstrated that the two policies outperform the baseline policies with both synthetic and realistic radar simulation datasets. The joint scheduling policy can exploit device correlations and thus performs better than the independent scheduling policy under strong correlations and strict communication constraints.