Precise evaluation of the isotope shift (IS) factors for seven low-lying potassium states is achieved using relativistic coupled-cluster theory. The energies of these states are compared with the experimental data to confirm the accuracy of wave functions calculated at different approximations and to highlight the significance of many-body and relativistic effects. Various methods are used to compute the IS factors, with the finite-field (FF) approach yielding results that align with observed and semiempirical data. This is attributed to orbital relaxation effects that are present naturally in the FF method but emerge only through perturbation in other methods. Using results from the FF approach, we review the mean-square-radius difference between \(^{38m}\)⁢K and \(^{39}\)K, which is combined with muonic atom x-ray spectroscopy and updated calculation of the nuclear polarizability effect to deduce the absolute radius of \(^{38m}\)⁢K. Finally, we evaluate the isospin symmetry breaking (ISB) in the isotriplet by integrating the radius of \(^{38m}\)⁢K with an updated radius of \(^{38}\)⁢Ca, concluding that the ISB is compatible with zero. This finding offers a stringent benchmark for nuclear models of ISB corrections in nuclear beta decay, which play a key role in determining the \(V_{ud}\) matrix element.