How does the Catholic Church reconcile Papal Infallibility with the biblical doctrine that "all have sinned" (Romans 3:23)?

In Romans 3:23, Scripture states that "all have sinned and fall short of the glory of God," a point emphasized throughout the New Testament regarding the universal human condition. However, the Catholic Church dogma of Papal Infallibility (defined during Vatican I) suggests that under specific conditions (ex cathedra), the Pope is preserved from error. From a Catholic theological perspective: Does the Church distinguish between impeccability (sinlessness) and infallibility (erroneous teaching)? If the Pope is considered a "sinner" like any other man, what is the scriptural or tradition-based mechanism that prevents his fallen nature from affecting these specific formal definitions of faith and morals? I am looking for an explanation of how these two concepts coexist in Catholic teaching without contradicting the biblical narrative of universal human fallibility