In this work, we envisage an evolution paradigm in a promising noncentrosymmetric one-dimensional zigzag chain structure, $(3\mathrm{AMP}){\mathrm{BiI}}_{5}$ [where AMP indicates (aminomethyl)piperidinium], through rigorous electronic structure calculations based on density functional theory (DFT). The electronic and optical properties along with the Rashba splitting and spin texture are systematically observed within the thermodynamic limit under compression equivalent to 9.6 GPa in this promising halide perovskite. Our study successfully reveals the intriguing transition of the electronic band structure from an indirect to a direct band gap phenomenon under compression in addition to an interesting redshift in the optical absorption spectra. To accurately describe the spin polarization both in plane and out of plane, we explore a three-dimensional Rashba model. The in-plane spin texture is found to arise from the octahedral distortion along the $b$ direction. The fundamental interplay between structural distortions and the Rashba splitting in the considered one-dimensional system under the influence of compression along with the evolution of spin texture could hold great potential for the pursuit of sustainable energy.