Context. Previous Gaia data releases offered the opportunity to uncover ultracool dwarfs (UCDs) through astrometric, rather than purely photometric, selection. The most recent, the third data release (DR3), offers in addition the opportunity to use low-resolution spectra to refine and widen the selection. Aims. In this work we use the Gaia DR3 set of UCD candidates and complement the Gaia spectrophotometry with additional photometry in order to characterise the global properties of the set. This includes the inference of the distances, their locus in the Gaia colour-absolute magnitude diagram, and the (biased through selection) luminosity function at the faint end of the main sequence. We study the overall changes in the Gaia RP spectra as a function of spectral type. We study the UCDs in binary systems, we attempt to identify low-mass members of nearby young associations, star-forming regions, and clusters, and we analyse their variability properties. Methods. We used a forward model and the Bayesian inference framework to produce posterior probabilities for the distribution parameters and a calibration of the colour index as a function of the absolute magnitude in the form of a Gaussian process. Additionally, we applied the hierarchical mode association clustering (HMAC) unsupervised classification algorithm for the detection and characterisation of overdensities in the space of celestial coordinates, projected velocities, and parallaxes. Results. We detect 57 young, kinematically homogeneous groups, some of which are identified as well-known star-forming regions, associations, and clusters of different ages. We find that the primary members of the 880 binary systems with a UCD belong to the thin and thick disc components of the Milky Way. We identify 1109 variable UCDs using the variability tables in the Gaia archive, 728 of which belong to the star-forming regions defined by HMAC. We define two groups of variable UCDs with extreme bright or faint outliers. Conclusions. The set of sources identified as UCDs in the Gaia archive contains a wealth of information that will require focused follow-up studies and observations. It will help advance our understanding of the nature of the faint end of the main sequence and the stellar-substellar transition.