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A hybrid system that combines cavity magnonics and cavity optomechanics is proposed to facilitate the generation of long‐distance entanglement and enable one‐way steering between magnons and phonons. This configuration involves two directly coupled cavities, with one interacting with magnons and the other coupling with a mechanical oscillator (i.e., phonons). By driving the microwave cavity with a weak squeezed vacuum field generated by a flux‐driven Josephson parametric amplifier, entanglement and one‐way steering can be further enhanced. Moreover, the results demonstrate that magnon–phonon entanglement and one‐way quantum steering exhibit robustness against temperature variations, which has significant implications for quantum information processing and storage. [ABSTRACT FROM AUTHOR]