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The superconducting behavior of transition-metal-embedded hexagonal boron-carbon (${\mathrm{B}}_{2}{\mathrm{C}}_{2}$) and boron-phosphorus (${\mathrm{B}}_{2}{\mathrm{P}}_{2}$) monolayers is systematically explored in both face-to-back (FB) and face-to-face (FF) stacking configurations. Embedding 3d and 4d transition metals into ${\mathrm{B}}_{2}{\mathrm{C}}_{2}$ and ${\mathrm{B}}_{2}{\mathrm{P}}_{2}$ frameworks induces robust metallicity, enabling superconductivity in these two-dimensional systems. Structural, dynamic, and energy stability are confirmed via formation energy analysis, phonon dispersion calculations, and ab initio molecular dynamics simulations, revealing several dynamically stable and nonmagnetic metallic phases: six $M\mathrm{BC}$ ($M=\mathrm{Sc}$, V, Y, Zr, Nb, Mo), seven $\mathrm{FF}\text{\ensuremath{-}}\mathrm{M}{\mathrm{B}}_{2}{\mathrm{C}}_{2}$, five $\mathrm{FB}\text{\ensuremath{-}}\mathrm{M}{\mathrm{B}}_{2}{\mathrm{P}}_{2}$, and eight $\mathrm{FF}\text{\ensuremath{-}}\mathrm{M}{\mathrm{B}}_{2}{\mathrm{P}}_{2}$ structures. By combining electron--phonon coupling analysis with the McMillan-Allen-Dynes formula and anisotropic Migdal--Eliashberg equations, we predict superconducting transition temperatures (${T}_{c}$) of up to 71.0 K for $\mathrm{FF}\text{\ensuremath{-}}\mathrm{Cu}{\mathrm{B}}_{2}{\mathrm{C}}_{2}$---featuring a distinct two-gap signature---and 31.5 K for MoBC with a single-gap profile, attributed to \ensuremath{\sigma}-bonding states and van Hove singularities, respectively. In comparison, ${\mathrm{B}}_{2}{\mathrm{P}}_{2}$-based systems show lower ${T}_{c}$ values up to 27.1 K (e.g., $\mathrm{FF}\text{\ensuremath{-}}\mathrm{Zr}{\mathrm{B}}_{2}{\mathrm{P}}_{2}$), attributed to weaker bonding interactions. A comprehensive comparison of atomic composition (C vs P) and stacking geometry highlights the critical role of covalency and electronic topology in governing superconducting properties, offering valuable guidance for the design of $\mathrm{high}\ensuremath{-}{T}_{c}$ two-dimensional superconductors.