Neutron stars, nature's densest laboratory, are a strange test bed for exploring the phase structure of strongly interacting matter under extreme conditions. Here we report a single framework that merges state-of-the-art effective field theories like chiral effective theory, dynamical mean-field treatments, and topological soliton models and numerical simulations at high resolution to construct a comprehensive equation of state (EoS) for neutron star matter. Our methodology bridges the gap between low-density hadronic domains and high-density deconfined quark phase by implementing a novel speedofsound interpolation framework that is firmly restricted by chiral effective theory and perturbative QCD predictions. Taking anisotropic pressure corrections, very strong magnetic fields, and rapid rotation into account, our framework accurately computes eminent macroscopic observables such as mass-radius relations, tidal deformabilities, and radial oscillation frequencies. Accurate simulations of binary neutron star mergers demonstrate that the development of quark-matter cores-marked by sudden polytropic index and sound speed jumps-imprints characteristic signatures on the post-merger gravitational wave spectrum. In particular, our research shows that such signatures in terms of alterations in the peaks of the dominant frequencies and alterations in the damping characteristics can be employed as a sensitive probe of the hadron-to-quark phase transition deep within the core of a neutron star. Our multimessenger approach synergistically combining state-of-the-art analytical techniques and observational data sets provides unprecedented knowledge of the microscopic properties of dense QCD matter. Not only do these discoveries further our understanding of the matter's underlying physics at supranuclear densities but also provide paths for experimental proof of quantum chromodynamics in its nonperturbative regime in the future using gravitational wave astrophysics and electromagnetic observations.