Magnetic fields are key to understand galaxy evolution, regulating stellar feedback and star formation in galaxies. We probe the origin of magnetic fields in late-type galaxies, measuring magnetic field strengths, exploring whether magnetic fields are only passive constituents of the interstellar medium, or whether they are active constituents being part of the local energy equilibrium. We measure equipartition magnetic field strengths in 39 galaxies from LoTSS-DR2 using LOFAR observations at 144MHz with 6arcsec angular resolution which (0.1-0.7kpc). For a subset of 9 galaxies, we obtain atomic and molecular mass surface densities using HI and CO(2-1) data, from the THINGS and HERACLES surveys, respectively. These data are at 13 arcsec angular resolution, which corresponds to 0.3-1.2kpc at the distances of our galaxies. We measure kinetic energy densities using HI and CO velocity dispersions. We found a mean magnetic field strength of 3.6-12.5uG with a mean of 7.9+/-2.0G across the full sample. The magnetic field strength has the tightest and steepest relation with the total gas surface density with B{prop.to}{Sigma}^0.309+/-0.006^_HI+H2_. The relation with the HI+H2 star-formation rate surface density and molecular gas surface density has significantly flatter slopes. After accounting for the influence of cosmic-ray transport, we found an even steeper relation of B{prop.to}{Sigma}^0.393+/-0.009^_HI+H2_. These results suggest that the magnetic field is regulated by a B-{rho} relation, which has its origin in the saturation of the small-scale dynamo. This is borne out by an agreement of kinetic and magnetic energy densities although local deviations do exist in particular in areas of high kinetic energy densities where the magnetic field is sub-dominant.