We show that the nonperturbative dynamics of $N=2$ super-Yang-Mills theories in a self-dual $\Omega$ background and with arbitrary simple gauge group is fully determined by studying renormalization group equations of vacuum expectation values of surface operators generating one-form symmetries. The corresponding system of equations is a nonautonomous Toda chain, the time being the renormalization group scale. We obtain new recurrence relations which provide a systematic algorithm computing multi-instanton corrections from the tree-level one-loop prepotential as the asymptotic boundary condition of the renormalization group equations. We exemplify by computing the $E_6$ and $G_2$ cases up to two instantons.