  We investigate the spacetime evolution of spin polarization within a
hydrodynamic framework based on the de Groot--van Leeuwen--van Weert
expressions for energy-momentum and spin tensors. The system's deviation from
boost invariance results in the interplay of different spin polarization
components, impacting spin observables. We specifically examine the transverse
momentum, azimuthal angle, and rapidity dependence of the mean spin
polarization vector of $\Lambda$ hyperons. Our results qualitatively align with
other models and experimental data on global spin polarization rapidity
dependence. While the quadrupole structure is absent in the longitudinal
component at midrapidity, our analysis reveals non-trivial signal at forward
rapidities that differs from predictions based on the Bjorken expansion.
