We present a multi-functional, bio-inspired polymer binder for silicon battery anodes that simultaneously achieves a predicted self-healing efficiency of >90% at room temperature and an internal lithium-ion diffusion coefficient exceeding 10^-8 cm^2/s. By incorporating biological sacrificial-bonding concepts from titin and nacre proteins, and utilizing a Directed Message Passing Neural Network (D-MPNN) surrogate, we screen 50,000 candidate SMILES strings in under 2.0 hours on consumer hardware, finding three specific structures matching all criteria (including LUMO >= 1.2 eV and swelling <= 20%) and eliminating the need for traditional multi-day DFT molecular dynamics computation. We verify the coupled dynamics of polymer healing, solvent swelling, ion transport, interfacial lamination adhesion, and electrolyte chemical compatibility via a 7D coupled ordinary differential equation (ODE) modeling framework and formalize the constraints in Lean 4.