The proliferation of diverse mission-critical applications places an urgent demand on elevated data rates, reduced latency and superior reliability for next-generation ultra-reliable low latency communication (URLLC) services. The simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) and rate-splitting multiple access (RSMA) technologies have emerged as potential technologies for future wireless networks to support greater coverage, stronger interference management and higher system performance. In this paper, we investigate the coupled phase-shift STAR-RIS aided RSMA system to enhance finite block length (FBL) transmission. Specifically, we focus on the optimization problem of sum throughput maximization via the joint optimization of the common rate allocation (CRA), beamforming matrix, and the transmission and reflection coefficients (TARC) matrix. Owing to the non-convexity of the optimization problem and the strong coupling of the variables, we employ the concept of alternating optimization (AO) to decompose the original problem into two easily solvable sub-problems: beamforming matrix and CRA optimization at base station (BS), TARC matrix optimization at STAR-RIS, which are resolved through the penalty function method and successive convex approximations (SCA). Simulation results validate that the proposed coupled phase-shift STAR-RIS aided RSMA scheme substantially boosts sum throughput relative to the benchmark methods, while satisfying the URLLC requirements.