Digital twins (DTs) of physical systems enable real-time remote tracking, control, and learning, but require to be updated with environmental sensory data to maintain alignment with their physical counterparts. In a network context, integrated sensing and communication (ISAC) capabilities can expand the DT's environmental awareness by linking received updates to the location where wireless sensors acquired them. Integrating localization services, however, increases the complexity of the communication system, and can only be supported through smart access optimization. To tackle this problem, we design a two-step goal-oriented approach: firstly, sensors with a high Value of Information (VoI) inform the network of their resource demands through a push-based random access; then, pull-based scheduled transmissions of the actual sensory data are optimized to satisfy ISAC performance constraints. This design allows to maximize the VoI of the information delivered to the DT while locating the transmitting nodes, significantly outperforming existing schemes.