Rare kaon decays offer a sensitive probe of short-distance physics and physics beyond the Standard Model. We study several key modes, including $K^+\to\pi^+\nu\bar\nu$, $K_L\to\pi^0\nu\bar\nu$, and $K_L\to\pi^0\ell^+\ell^-$, focusing on new physics contributions mediated by semileptonic $(V-A)\otimes(V-A)$ operators. A global analysis of current data is presented together with projections based on future sensitivities expected from NA62 and KOTO-II. We show that charged-lepton modes play an essential role in lifting degeneracies present in neutrino observables and significantly enhance sensitivity to short-distance effects.