Targeting the delay-constrained Internet-of-Things (IoT) applications in sixth-generation (6G) networks, in this paper, we study the integration of simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) and non-orthogonal multiple access-based backscatter communication (BAC-NOMA) under statistical delay quality-of-service (QoS) requirements. In particular, we derive the closed-form expressions for the effective capacity of the STAR-RIS assisted BAC-NOMA system under Nakagami-m fading channels and energy-splitting protocol of STAR-RIS. Our simulation results demonstrate the effectiveness of STAR-RIS over the conventional RIS (C-RIS) and show an excellent correlation with analytical results, validating our analysis. The results reveal that the stringent QoS constraint degrades the effective capacity; however, the system performance can be improved by increasing the STAR-RIS elements and adjusting the energy-splitting coefficients. Finally, we determine the optimal pair of power reflection coefficients subject to the per-BSN effective capacity requirements.