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MgB2, a phonon-mediated superconductor with record-high critical temperature Tc ≃ 39 K, is revisited to obtain a comprehensive theory of electrons, phonons, and their coupling with minimal ab initio input. We construct compact analytic models for the electronic structure, phonons, and electron-phonon coupling (EPC) of MgB2. We show that strong in-plane B sp2 bonding realizes an obstructed band structure whose natural description is a bond-centered kagome lattice, yielding small quasi-2D σ-band Fermi-surface cylinders and pronounced quantum-geometric effects. The phonon spectrum is found to closely track that of a graphene-like boron layer, but the heavy intercalated Mg atoms dominate the three acoustic branches and rigidly lift the boron modes into the optical sector, while the in-plane B–B bond-stretching mode exhibits a pronounced softening along Γ–A. By symmetry, this Γ-point bond-stretching mode is the only Γ phonon that can couple to the σ Fermi surface, explaining its dominant contribution to the EPC. Upon electron doping toward the doubly degenerate band edge of the σ sheets, we find that a reduced density of states competes with enhanced EPC matrix elements. At light electron doping, ab initio calculations show that the EPC enhancement dominates, leading to an increase in Tc (within the clean doping limit without disorder effects). Using the Gaussian approximation for the EPC tensor, we further show that this enhancement is overwhelmingly quantum geometric in origin, arising from a geometric EPC contribution of the small σ Fermi surface peaked at Γ. Overall, our results provide a transparent, symmetry-based account of superconductivity in MgB2 and suggest that quantum-geometric effects can be essential for shaping doping trends in phonon-mediated superconductors.