The sub-Planck structures in phase space are extremely fragile interference patterns that serve as distinctive quantum signatures, with applications in precision metrology and quantum sensing. While such structures have been frequently studied with coherent-state superposition, their emergence in squeezed states, among the most fundamental and experimentally accessible nonclassical states, remains comparatively unexplored. In this work, we introduce a class of superposition of squeezed states that are inherently devoid of sub-Planck structure. We further investigate their engineering through non-Gaussian operations of photon addition and subtraction. Our analytical and numerical results reveal that these operations, well-known to enhance nonclassicality, induce clear sub-Planck structures, which for any even or odd component number beyond $M>2$ can exhibit isotropic structures and enhanced sensitivity. Here, isotropy becomes a feature of quantum resource rather than of the geometry, providing more flexibility in engineering quantum states for precision metrology. These isotropic features become more pronounced with an increasing number of squeezed components and an increasing number of photons added or subtracted. Moreover, photon addition is shown to produce finer and more pronounced interference fringes than photon subtraction, leading to stronger sensitivity to small displacements in phase space. As a notable outcome, we identify the four-component squeezed state as the squeezed counterpart of the original compass state and demonstrate that unlike the anisotropic compass state, it exhibits nearly isotropic sub-Planck structures together with enhanced quantum sensitivity. These findings not only advance the fundamental understanding of quantum phase-space engineering but also position the engineered squeezed superposition as a versatile platform for quantum sensing and precision parameter estimation beyond the standard quantum limit.

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• Quantum optics