We consider an unsourced random access (URA) system enhanced with a feedback mechanism that serves both communication and sensing tasks. While traditional URA systems do not incorporate feedback, we propose a novel feedback signal design that announces the decoding status of users and simultaneously enables target sensing. To design this dual-purpose feedback, we introduce a modified projected gradient descent algorithm that minimizes a weighted combination of communication and sensing errors. Simulation results show that the proposed feedback design outperforms the state-of-the-art feedback design in the URA literature. Furthermore, we illustrate the trade-off between communication and sensing capabilities, offering valuable insight into balancing these two tasks.