  Superconductor-semiconductor hybrid devices, involving quantum dots
interfaced with floating and/or grounded superconductors, have reached a level
of complexity which calls for the development of versatile and numerically
efficient modelling tools. Here, we propose an extension of the surrogate model
solver for sub-gap states [Phys. Rev. B 108, L220506 (2023)], which is able to
handle floating superconducting islands with finite charging energy. Upon
eliminating all finite-size effects of the computationally demanding Richardson
model approach, we achieve a more efficient way of calculating the sub-gap
spectra and related observables without compromising their accuracy. We provide
a number of benchmarks between the two approaches and showcase the versatility
of the extended surrogate model solver by studying the stability of
spin-triplet ground states in various tunable devices. The methods introduced
here set the stage for reliable microscopic simulations of complex
superconducting quantum circuits across all their relevant parameter regimes.
