<p>Recent wireless communication systems increasingly adopt wireless power transfer, non-orthogonal multiple access (NOMA), and reconfigurable intelligent surfaces (RIS) to enhance spectral efficiency and support energy-constrained devices for future 6G networks. However, wireless-powered D2D cellular systems still face challenges such as limited harvested energy, strict uplink quality-of-service (QoS) requirements, and the trade-off between reliability and spectral efficiency. Moreover, conventional RIS only supports users on one side of the surface, restricting coverage flexibility. To address these issues, this paper investigates a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided cooperative D2D cellular network, where two single-antenna D2D users located on opposite sides of STAR-RIS harvest energy from the base station (BS) during the downlink phase and transmit information in the following two phases. An energy-based decision-making scheme is proposed to determine whether NOMA should be deployed through power allocation for superposition signals of the BS and D2D user. This strategy ensures cellular uplink QoS in power-limited conditions while enabling D2D cooperation when sufficient energy is harvested. STAR-RIS is applied in both energy transfer and information transmission phases to exploit its 360° coverage capability. Closed-form expressions for outage probability, sum throughput, energy efficiency, and sum ergodic capacity are derived, along with an asymptotic analysis of sum throughput for further insights. Monte Carlo simulations validate the theoretical results and demonstrate the effects of STAR-RIS elements, STAR-RIS coefficients, energy thresholds, and NOMA power allocation on system performance.</p>