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Next-generation wireless applications are expected to enable extended ultra-reliable low-latency communication (URLLC) to support high data rates along with ultra-reliability and low-latency features beyond the capabilities of existing core services. There is a need to transition from conventional architectures to more efficient and robust multiple-access schemes to meet these consolidated requirements in resource-constrained systems. This study explores the utilization of simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) in non-orthogonal multiple access (NOMA) systems to enable spectrally efficient URLLC, even under the imperfect channel state information. In particular, we focus on maximizing spectral efficiency by jointly designing robust beamforming at the base station and STAR-RIS subject to given URLLC requirements. Due to the non-convexity of the formulated problem, we propose an alternating optimization framework that obtains sub-optimal solutions to the problems of beamforming design at the BS and STAR-RIS, respectively by exploiting $\mathcal {S}-$ procedure and successive convex approximation. Simulation results confirm that the STAR-RIS-NOMA system can significantly boost the spectral efficiency by 10-15% compared to conventional reflecting-only RIS while guaranteeing the strict URLLC requirements. Specifically, among all the possible modes of STAR-RIS, the time-splitting mode provides better spectral efficiency than other modes owing to its better interference management.