Context. Gaseous halos play a key role in understanding inflow, feedback, and the overall baryon budget in galaxies. Literature models predict transitions of the state of the gaseous halo between cold and hot accretion, winds, fountains, and hydrostatic halos at certain galaxy masses. Since luminosities of radio AGN are sensitive to halo densities, any significant transition would be expected to show up in the radio luminosities of large samples of galaxies. The LOw Frequency ARray (LOFAR) Two-Metre Sky Survey (LoTSS) has identified a galaxy stellar mass scale, 10¹¹ M_⊙, above which the radio luminosities increase disproportionately. Aims. We investigate if radio luminosities of galaxies, especially the marked rise at galaxy masses around 10¹¹ M_⊙, can be explained with standard assumptions regarding jet powers, scaling between black hole mass and galaxy mass, and gaseous halos. Methods. Based on observational data and theoretical constraints, we developed models for the radio luminosity of radio AGN in halos under infall, galactic wind, and hydrostatic conditions. We compared these models to LoTSS data for a large sample of galaxies in the mass range between 10^8.5 M_⊙ and 10¹² M_⊙. Results. Under the assumption that the same characteristic upper limit to jet powers known from high galaxy masses holds at all masses, we find the maximum radio luminosities for the hydrostatic gas halos to lie close to the upper envelope of the distribution of the LOFAR data. The marked rise in radio luminosity at 10¹¹ M_⊙ is matched in our model and is related to a significant change in halo gas density around this galaxy mass, which is a consequence of lower cooling rates at a higher virial temperature. Wind and infall models overpredict the radio luminosities for small galaxy masses and have no particular steepening of the run of the radio luminosities predicted at any galaxy mass. Conclusions. Radio AGN could have the same characteristic Eddington-scaled upper limit to jet powers in galaxies of all masses in the sample if the galaxies have hydrostatic gas halos in phases when radio AGN are active. We find no evidence of a change of the type of galaxy halo with the galaxy mass. Galactic winds and quasi-spherical cosmological inflow phases cannot frequently occur at the same time as powerful jet episodes unless the jet properties in these phases are significantly different from what we assumed in our model.