Gravito-inertial asteroseismology saw its birth thanks to high-precision CoRoT and Kepler space photometric light curves. So far, it gave rise to the internal rotation frequency of a few hundred intermediate-mass stars, yet only several tens of these have been weighed, sized, and age-dated with high precision from asteroseismic modelling. We aim to increase the sample of optimal targets for future gravito-inertial asteroseismology by assessing the properties of 15062 newly found Gaia DR3 gravity-mode pulsators.We also wish to investigate if there is any connection between their fundamental parameters and dominant mode on the one hand, and their spectral line broadening measured by Gaia on the other hand. After re-classifying about 22% of the F-type gravity-mode pulsators as B-type according to their effective temperature, we construct histograms of the fundamental parameters and mode properties of the 15062 new Gaia DR3 pulsators. We compare these histograms with those of 63 Kepler bona fide class members.We fit errors-in-variables regression models to couple the effective temperature, luminosity, gravity, and oscillation properties to the two Gaia DR3 parameters capturing spectral line broadening for a fraction of the pulsators. We find that the selected 15062 gravity-mode pulsators have properties fully in line with those of their well-known Kepler analogues, revealing that Gaia has a role to play in asteroseismology. The dominant g-mode frequency is a significant predictor of the spectral line broadening for the class members having this quantity measured. We show that the Gaia vbroad parameter captures the joint effect of time-independent intrinsic and rotational line broadening and time-dependent tangential pulsational broadening. While the Gaia mission was not designed to detect non-radial oscillation modes, its multitude of data and homogeneous data treatment allow us to identify a vast amount of new gravity-mode pulsators having fundamental parameters and dominant mode properties in agreement with those of such Kepler bona fide pulsators. This large new sample of Gaia DR3 pulsators can be followed up with dedicated high-precision photometric or high-resolution spectroscopic instruments to embark upon asteroseismic modelling.