Quantum magnonics presents significant potential for advancing quantum sensors through magnon–photon coupling. In this research, we experimentally and theoretically study the microwave-mediated coherent coupling in a system combined by a superconducting resonator chip and quasi-two-dimensional topological magnets Cu[1,3-benzenedicarboxylate(bdc)]. By changing the orientation of the Cu(1,3-bdc) flakes on the chip, coherent level repulsion of two different magnon modes is demonstrated. Our measurements indicate that magnon modes in two anisotropic Cu(1,3-bdc) flakes interact with each other by the mediation of cavity photons, with the coupling energy transfer conforming to the “magnon-loss-resistor” model. Our research offers a pathway to investigate spin dynamics in innovative quantum materials, facilitating magnon–photon coupling for effective quantum operations.