Integrated sensing and communications (ISAC) is a promising technology for the sixth generation (6G) of mobile communications. High-precision positioning through sensing can significantly enhance subsequent communication for mobile users. This study proposes a method extracting spatial location information using estimated channel state information (CSI) to solve the simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR- RIS)-assisted bilateral user localization problem. Existing neural network-based localization algorithms suffer from low accuracy and difficulty distinguishing users in similar areas. In contrast, this paper pioneeringly proposed the CsiNet-Former network, which achieves accurate user three-dimensional (3D) location estimation and trajectory prediction by extracting spatial feature information from CSI in a few time slots. This paper also compares the impact of the STAR-RIS in different modes on user localization accuracy. Simulation results show that the proposed method accurately locates and predicts the trajectory of bilateral users in the energy splitting (ES) mode using one set of network parameters under a suitable energy splitting ratio. CsiNet-Former achieves an average bilateral localization and prediction error of 0.75 m, with a single-side error of 0.034 m, outperforming existing location methods while covering a larger detectable area.