We present 353 GHz full-sky maps of the polarization fraction $p$, angle $psi$, and dispersion of angles $S$ of Galactic dust thermal emission produced from the 2018 release of Planck data. We confirm that the mean and maximum of $p$ decrease with increasing $N_H$. The uncertainty on the maximum polarization fraction, $p_mathrm{max}=22.0$% at 80 arcmin resolution, is dominated by the uncertainty on the zero level in total intensity. The observed inverse behaviour between $p$ and $S$ is interpreted with models of the polarized sky that include effects from only the topology of the turbulent Galactic magnetic field. Thus, the statistical properties of $p$, $psi$, and $S$ mostly reflect the structure of the magnetic field. Nevertheless, we search for potential signatures of varying grain alignment and dust properties. First, we analyse the product map $S times p$, looking for residual trends. While $p$ decreases by a factor of 3--4 between $N_H=10^{20}$ cm$^{-2}$ and $N_H=2times 10^{22}$ cm$^{-2}$, $S times p$ decreases by only about 25%, a systematic trend observed in both the diffuse ISM and molecular clouds. Second, we find no systematic trend of $S times p$ with the dust temperature, even though in the diffuse ISM lines of sight with high $p$ and low $S$ tend to have colder dust. We also compare Planck data with starlight polarization in the visible at high latitudes. The agreement in polarization angles is remarkable. Two polarization emission-to-extinction ratios that characterize dust optical properties depend only weakly on $N_H$ and converge towards the values previously determined for translucent lines of sight. We determine an upper limit for the polarization fraction in extinction of 13%, compatible with the $p_mathrm{max}$ observed in emission. These results provide strong constraints for models of Galactic dust in diffuse gas.
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