The critical step for future quantum industry demands realization of efficient information exchange between different-platform hybrid systems, including photonic and magnonic systems, that can harvest advantages of distinct platforms. The major restraining factor for the progress in certain hybrid systems is the fundamentally weak coupling parameter between the elemental particles. This restriction impedes the entire field of hybrid magnonics by making realization of scalable on-chip hybrid magnonic systems unattainable. In this work, we propose a general flexible approach for realization of on-chip hybrid magnonic systems with unprecedentedly strong coupling parameters. The approach is based on multilayered micro-structures containing superconducting, insulating and ferromagnetic layers with modified both photon phase velocities and magnon eigen-frequencies. Phenomenologically, the enhanced coupling strength is provided by the radically reduced photon mode volume. The microscopic mechanism of the phonon-to-magnon coupling in studied systems evidences formation of the long-range superconducting coherence via thick strong ferromagnetic layers. This coherence is manifested by coherent superconducting screening of microwave fields by the superconductor/ferromagnet/superconductor three-layers in presence of magnetization precession. This discovery offers new opportunities in microwave superconducting spintronics for quantum technologies.