Theoretical Prediction of optimal $T_c$ for Nickelate $\mathrm{L}{\mathrm{a}}_{3-\mathrm{x}}\mathrm{S}{\mathrm{m}}_{\mathrm{x}}\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_{7-\delta }$

Recently, the nickel-based superconductor $T_c$ record was updated to $96\text{ K}$ in bilayer $\mathrm{L}{\mathrm{a}}_{3-\mathrm{x}}\mathrm{S}{\mathrm{m}}_{\mathrm{x}}\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_{7-\delta }$ (LSNO) under pressure, raising a critical question: Can its $T_c$ exceed the 164 K benchmark of copper-based superconductors? We find that both monoclinic and tetragonal LSNO have an octahedral quantum well structure (determining $T_c$) nearly identical to $\mathrm{Y}\mathrm{B}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ (YBCO). Based on the formula $T_c=\mathrm{\Lambda }\mathrm{/}{\xi }^2$ (Planck ground-state quantum well oscillator hypothesis, $\xi$ = lattice parameter-determined quantum well depth), we predict Sm-doped nickelate $T_c$ values of $93.4\text{ K}$ (monoclinic) and $97.1\text{ K}$ (tetragonal), in excellent agreement with experimental data ($92\text{ K}$ and $96\text{ K}$). Notably, despite distinct composition and symmetry (LSNO: $P{2}_1\mathrm{/}m$; YBCO: $Pmmm$), their $\xi$ ($3.6629\mathring{A}$ vs $3.6720\mathring{A}$) and $T_c$ ($92\text{ K}$ vs $93\text{ K}$) are nearly identical. This validates the proposed superconducting formula and unifies copper-based and nickel-based superconductors at the angstrom-scale octahedral quantum well. Further predictions indicate the maximum achievable $T_c$ for lanthanide-based nickelates (regardless of layer number) is $\sim 100\text{ K}$.