Context. Small planets located at the lower mode of the bimodal radius distribution are generally assumed to be composed of iron and silicates in a proportion similar to that of the Earth. However, recent discoveries are revealing a new group of low-density planets that are inconsistent with that description. Aims. We intend to confirm and characterize the TESS planet candidate TOI-244.01, which orbits the bright (K = 7.97 mag), nearby (d = 22 pc), and early-type (M2.5 V) M-dwarf star GJ 1018 with an orbital period of 7.4 days. Methods. We used Markov chain Monte Carlo methods to model 57 precise radial velocity measurements acquired by the ESPRESSO spectrograph together with TESS photometry and complementary HARPS data. Our model includes a planetary component and Gaussian processes aimed at modeling the correlated stellar and instrumental noise. Results. We find TOI-244 b to be a super-Earth with a radius of Rp = 1.52 ± 0.12 R and a mass of Mp = 2.68 ± 0.30 M. These values correspond to a density of ρ = 4.2 ± 1.1 g cm-3, which is below what would be expected for an Earth-like composition. We find that atmospheric loss processes may have been efficient to remove a potential primordial hydrogen envelope, but high mean molecular weight volatiles such as water could have been retained. Our internal structure modeling suggests that TOI-244 b has a 479-96+128 km thick hydrosphere over a 1.17 ± 0.09 R solid structure composed of a Fe-rich core and a silicate-dominated mantle compatible with that of the Earth. On a population level, we find two tentative trends in the density-metallicity and density-insolation parameter space for the low-density super-Earths, which may hint at their composition. Conclusions. With a 8% precision in radius and 12% precision in mass, TOI-244 b is among the most precisely characterized super-Earths, which, together with the likely presence of an extended hydrosphere, makes it a key target for atmospheric observations.