The search for the primordial B-modes of the cosmic microwave background (CMB) relies on the separation from the brighter foreground dust signal. In this context, the characterization of the spectral energy distribution (SED) of thermal dust in polarization has become a critical subject of study. We present a power-spectra analysis of Planck data, which improves upon previous studies by using the newly released SRoll2 maps that include corrections on residual data systematics and by extending the analysis to regions near the Galactic plane. Our analysis focuses on the lowest multipoles between `=4 and 32, as well as three sky areas with sky fractions of fsky = 80%, 90%, and 97%. The mean dust SED for polarization and the 353 GHz Q and U maps are used to compute residual maps at 100, 143, and 217 GHz, highlighting variations of the dust polarization SED on the sky and along the line of sight. Residuals are detected at the three frequencies for the three sky areas. We show that models based on total-intensity data end up underestimating (by a significant factor) the complexity of dust polarized CMB foreground. Our analysis emphasizes the need to include variations of the polarization angles of the dust polarized CMB foreground. The frequency dependence of the EE and BB power spectra of the residual maps yields further insight. We find that the moments expansion to the first order of the modified black-body (MBB) spectrum provides a good fit to the EE power-spectra. This result suggests that the residuals could follow mainly from variations of the dust MBB spectral parameters. However, this conclusion is challenged by cross-spectra showing that the residuals maps at the three frequencies are not fully correlated, as well as the fact that the BB power-spectra do not match the first order moment expansion of a MBB SED. This work sets new requirements for simulations of the dust-polarized foreground and component separation methods, showing that a significant refinement to the dust modeling is necessary to ensure an unbiased detection of the CMB primordial B-modes at the precision required by future CMB experiments. Further works would also be required to theoretically model the impact of polarization-angle variations on the EE and BB power spectra of residual maps.