2002 VW Passat 1.8T Persistent P0171 Code - Solutions and Fixes

I own a 2002 Volkswagen Passat with the 1.8L T engine and have been experiencing a recurring P0171 fault code. Despite addressing two key issues, the code continues to appear after resetting the check engine light. First, I identified and repaired a split and cracked manifold breather tube — the hose connecting the intake manifold to the coolant reservoir (approximately 6 inches long). This component was allowing uncontrolled air into the intake system, which can trigger the P0171 code. Second, I replaced the 'air pump' that this hose connects to. The original unit was found to be in two separate pieces and was also contributing to unregulated airflow into the engine management system. This part is connected to three hoses in total. I've thoroughly inspected all other hoses and connections throughout the engine bay with no additional damage or leaks detected. The vehicle has accumulated 65,000 miles. Even after multiple resets of the check engine light, the P017-1 code persists. I'm seeking advice on further troubleshooting steps to resolve this issue permanently.