Conventional mobile networks, including both localized cell-centric and cooperative cell-free networks (CCN/CFN), are built upon rigid network topologies. However, neither architecture is adequate to flexibly support distributed integrated sensing and communication (ISAC) services, due to the increasing difficulty of aligning spatiotemporally distributed heterogeneous service demands with available radio resources. In this paper, we propose an elastic network topology (ENT) for distributed ISAC service provisioning, where multiple co-existing localized CCNs can be dynamically aggregated into CFNs with expanded boundaries for federated network operation. This topology elastically orchestrates localized CCN and federated CFN boundaries to balance signaling overhead and distributed resource utilization, thereby enabling efficient ISAC service provisioning. A two-phase operation protocol is then developed. In Phase I, each CCN autonomously classifies ISAC services as either local or federated and partitions its resources into dedicated and shared segments. In Phase II, each CCN employs its dedicated resources for local ISAC services, while the aggregated CFN consolidates shared resources from its constituent CCNs to cooperatively deliver federated services. Furthermore, we design a utility-to-signaling ratio (USR) to quantify the tradeoff between sensing/communication utility and signaling overhead. Consequently, a USR maximization problem is formulated by jointly optimizing the network topology (i.e., service classification and CCN aggregation) and the allocation of dedicated and shared resources. However, this problem is challenging due to its distributed optimization nature and the absence of complete channel state information. To address this problem efficiently, we propose a multi-agent deep reinforcement learning (MADRL) framework with centralized training and decentralized execution.