Yes, President Trump did negotiate with the Taliban. He had conditions, a shared government, not attacking American troops or citizens, and no taking additional territory by force. When they broke one of the conditions, Trump had them bombed and they stopped.
President Trump also had a plan on the order of withdrawal, first, removing citizens, destroying equipment, destroying bases, then lastly, removing the troops. Biden did everything wrong. Biden did not follow Trump's plan, he ignored Trump's agreement with the Taliban, and changed the dates, pissing off the Taliban leadership.
As far as the Afgan military, without American leadership, the Afgan army is a joke. Most of the members of the Army were only there to get a paycheck. They were not dedicated to the country, government, or democracy. The Afgan leadership and government are corrupt top to bottom, so the soldiers were not going to die for them.
Nobody is faulting the Biden/Harris regime for following President Trump's desire to get out of Afghanistan. Biden is being ridiculed and hammered for the abysmal execution of the withdrawal, lack of communication and coordination with our allies, and the total lack of planning.