We propose a unified high-fidelity and reduced-order modeling framework for the bending analysis of thin flooring panels consisting of orthotropic Kirchhoff–Love plates resting on Winkler-type elastic foundations, with internal contact mechanics enforced via penalty-based interface coupling. The full-order model (FOM) employs a multipatch C⁰ interior-penalty discontinuous Galerkin discretization using high-order Lagrange finite elements (p ≥ 2), which naturally accommodates complex geometries, domain decomposition, and the weak enforcement of interface conditions for both the relative transverse displacement and rotation between adjacent panels. The plate–foundation interaction is modeled by a smooth, penalized Winkler law that distinguishes compression from uplift and maintains differentiability [Wells2007]. Parametric dependencies include the plate's geometric and constitutive parameters, the foundation's stiffness, and spatially varying loads, enabling comprehensive digital-twin analyses. To enable real-time predictions, we derive two complementary reduced-order surrogates via Proper Orthogonal Decomposition (POD). First, an intrusive POD-Galerkin ROM is obtained by projecting the assembled full-order operators onto a reduced basis of orthonormal modes; the resulting low-dimensional nonlinear system is solved via a projected Newton solver [Rozza]. Second, a non-intrusive POD-NN model exploiting a feedforward neural network maps normalized physical parameters directly to retained POD coefficients, yielding great generalization across the parameter domain [Hesthaven]. Both reduced models accurately reproduce full-order responses while enabling real-time and many-query evaluations. The framework is validated on benchmark problems involving rectangular orthotropic plates under uniform, localized, and multi-patch loading, with foundation stiffness varied over two orders of magnitude. Results exhibit optimal h^{p+1} convergence in the L²-norm for the FOM, and ROM predictions maintain relative errors well within desired limits.