What can be learnt from UHECR anisotropies observations Paper III: Update with new data and Galactic magnetic fields models

Context. At large angular scales, the Pierre Auger Observatory has reported a significant dipole modulation in right ascension, while at intermediate angular scales, localized flux excesses have been identified by both the Auger and Telescope Array collaborations. These observations were investigated in the first two papers of this series. Aims. We examine the implications of these anisotropy measurements and assess to what extent they can be used to constrain the origin of UHECRs and the astrophysical or physical parameters of viable source scenarios. Methods. As in the first two papers of this series, we generate realistic UHECR sky maps for a wide range of astrophysical models consistent with current spectral and composition constraints, assuming that UHECR sources trace the distribution of galaxies in the Universe. We update our previous studies by incorporating the most recent models of the Galactic magnetic field and apply the same large- and intermediate-scale anisotropy analyses as those used by the Auger Collaboration to simulated datasets with current experimental exposure. Results. The main novelty of this third paper is the improved compatibility between simulations and data, in particular regarding the reconstructed dipole direction, when using several of the recently proposed Galactic magnetic field models. Despite this progress, our main conclusions remain unchanged: although the observed anisotropies are compatible with an extragalactic origin of UHECRs, present data and magnetic-field uncertainties do not allow strong constraints to be placed on the nature, spatial distribution, or density of UHECR sources. Conclusions. Further progress in the interpretation of UHECR anisotropies will require improved constraints on cosmic magnetic fields, advances in source modeling, and significantly larger experimental exposures