We present a detailed analysis of integrated correlators for an \( \mathcal{N}=2 \) supercon-formal field theory on a squashed sphere with SU(N) gauge group and fundamental/anti-symmetric matter. Employing the matrix model arising from supersymmetric localisation, we compute derivatives of the partition function \( \mathcal{Z} \) with respect to the fundamental mass (μ), the anti-symmetric mass (m) and the squashing parameter (b), corresponding to integrated insertions of the \( \mathcal{N}=2 \) flavour-current and stress-tensor multiplets, which are holographically dual to gluon and graviton scatterings in the presence of D7-branes. For correlators dual to only graviton scatterings, we confirm the planar-limit equivalence with \( \mathcal{N}=4 \) SYM. Our main result is a remarkable universality for the mixed gluon-graviton scattering amplitudes off D7-branes, obtained from \( {\partial}_{\mu}^2{\partial}_m^2\log \mathcal{Z} \) and \( {\partial}_{\mu}^2{\partial}_b^2\log \mathcal{Z} \) . We show that the leading and sub-leading large-N contributions in the strong-coupling regime are governed by universal asymptotic series, identical to those found for integrated giant-graviton correlators in \( \mathcal{N}=4 \) SYM. We also propose an SL(2, ℤ)-invariant completion of these results in terms of non-holomorphic Eisenstein series. This completion provides exact constraints on higher-derivative terms in the dual AdS5 brane-string amplitudes and highlights an unexpected universality across distinct superconformal theories at strong coupling.
