The increasing demand for cost-effective, high-speed Internet of Things (IoT) applications in the coming sixth-generation (6G) networks has driven research toward maximizing spectral efficiency and simplifying hardware designs. In this context, we investigate the sum rate maximization problem for a mode-switching discrete-phase shifters simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided multi-antenna access point network, emphasizing hardware efficiency and reduced cost. A mixed-integer nonlinear optimization framework is formulated for joint optimization of the active beamforming matrix, user power allocation, and STAR-RIS phase shift vectors, including binary transmission/reflection amplitudes and discrete phase shifters. To solve the formulated problem, we employ a block coordinate descent method, dividing it into three subproblems tackled using difference-of-concave programming and combinatorial optimization techniques. Numerical results validate the effectiveness of the proposed joint optimization approach, consistently achieving superior sum rate performance compared to partial optimization methods, thereby underscoring its potential for efficient and scalable 6G IoT systems.