We consider an unsourced random access (URA) system enhanced with a feedback mechanism that serves both communication and sensing tasks. Specifically, the base station employs a multi-antenna array to receive user transmissions and to broadcast a finite-length downlink feedback signal that informs users about their decoding status. Opportunistically, by processing the reflections of this same feedback signal, the base station is also able to estimate the directions of targets present in the environment. 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.