PO420 Fault in 2001 Pontiac Grand Prix: Catalyst System Efficiency Below Threshold - What Does It Mean and How to Fix?

I own a 2001 Pontiac Grand Prix SE and my Check Engine Light has come back on after being temporarily fixed. The diagnostic tool shows code PO420 — Catalyst System Efficiency Below Threshold (Bank 1). I took the car to a repair shop, where they advised a full tune-up would turn off the light. After replacing the catalytic converter and completing the tune-up, the Check Engine Light went out. However, about two hours later, it reappeared. The technician reset the system, but the code PO420 returned shortly after. My question is: Does this mean there's still an issue with the catalytic converter? Is it true that a full tune-up should be performed when replacing a catalytic converter? And how costly is this repair? I want to understand what exactly PO42 or 420 means and whether the problem lies in the converter, the engine, or another component. Any insights from owners of similar vehicles would be greatly appreciated. Thanks for your help!