This study models the macroeconomic impacts of state-backed Central Bank Digital Currencies (CBDCs) on domestic financial stability, focusing specifically on their transmission via monetary velocity. Utilizing a modified New Keynesian Dynamic Stochastic General Equilibrium (DSGE) framework calibrated to a standard fractional-reserve banking economy, we simulate the introduction of an interest-bearing retail CBDC. The findings reveal a dual-effect paradox: CBDCs significantly accelerate transaction velocity by eliminating clearing frictions, which boosts short-term aggregate demand and payment system efficiency. However, this increased velocity accelerates structural bank disintermediation, compressing the money multiplier and driving up commercial banking funding costs by an average of 140 basis points under economic stress. Our simulations demonstrate that during macroeconomic shocks, the absence of friction converts routine reallocations into high-velocity digital bank runs. To reconcile this efficiency-stability trade-off, we model regulatory interventions and prove that a calibrated, tiered holding cap (e.g., 3,000 currency units) successfully mitigates systemic disintermediation risks, preserving credit supply to the real economy without sacrificing the transactional benefits of sovereign digital money.