HdC and EHe stars through the prism of Gaia DR3 3D distribution and Gaia's chromatic PSF effects

Context. Upon its release the Gaia DR3 catalogue has led to tremendous progress in multiple fields of astronomy by providing the complete astrometric solution for nearly 1.5 billion sources. Aims. We analysed the photometric and astrometric results for Hydrogen-deficient Carbon (HdC), Extreme Helium (EHe), and DYPer type stars to identify any potential biases. This analysis aimed to select stars suitable for kinematic and spatial distribution studies. Methods. We investigated the information obtained from the Gaia image parameter determination (IPD) process, which was cross-matched with Gaia light curves. One main objective was to understand the impact of photometric declines in R Coronae Borealis (RCB) stars on Gaia astrometry. Results. Based on the evidence gathered, we have reached the conclusion that the astrometric fits for numerous RCB stars, including R CrB itself, are not valid due to the Gaia point spread function (PSF) chromaticity effect in both shape and centroid. The astrometric results of all stars with a significant time-dependent colour variation should be similarly affected. RCB stars might thus be promising sources to correct this effect in future Gaia releases. Furthermore, after validating the Gaia astrometric results for 92 stars, we observed that the majority of HdC and EHe stars are distributed across the three old stellar structures, the thick disk, the bulge and the halo. However, we have also uncovered evidence indicating that some HdC and EHe stars exhibit orbits characteristic of the thin disk. This is also particularly true for all DYPer type stars under study. Finally, we have produced a list of star memberships for each Galactic substructure, and provided a list of heliocentric radial velocities and associated errors for targets not observed by Gaia DR3. Conclusions. We are beginning to observe a relationship between kinematics, stellar population, and metallicity in RCB and EHe stars. That relation can be explained, within the double degenerate scenario, by the large range in the delay time distribution expected from population synthesis simulations, particularly through the HybCO merger channel.