Strong electron correlations drive Mott insulator transitions. Yet, there exists no framework to classify Mott insulators by their degree of correlation. Cuprate superconductors, with their tunable doping and rich phase diagrams, offer a unique platform to investigate the evolution of these interactions. However, spectroscopic access to a clean half-filled Mott-insulating state is lacking in compounds with the highest superconducting onset temperature. To fill this gap, we introduce a pristine, half-filled thallium-based cuprate system, Tl2Ba5Cu4Ox. Using high-resolution resonant inelastic x-ray scattering, we probe long-lived magnon excitations and uncover a pronounced kink in the magnon dispersion, marked by a simultaneous change in group velocity and lifetime broadening. Modeling the dispersion within a Hubbard-Heisenberg approach, we extract the interaction strength and compare it with other cuprate systems. Our results establish a cuprate universal relation between electron-electron interaction and magnon zone-boundary dispersion. Superconductivity seems to be optimal at intermediate correlation strength, suggesting an optimal balance between localization and itinerancy.