Afghanistan War Commission Act of 2021 This bill establishes the independent Afghanistan War Commission within the legislative branch. The commission must conduct a study of various matters related to U.S. operations and activities in Afghanistan, including (1) U.S. military, diplomatic, development and intelligence objectives from September 1, 1996, to August 30, 2021; (2) the efficacy of U.S. efforts to meet such objectives; (3) the factors that led to the collapse of the Afghan National Defense Security Forces in 2021; and (4) the efficacy of efforts to fight corruption. The commission must annually report to Congress on the progress of its study. Within three years (with an extension of up to one year available) of the commission's first meeting, it must submit to Congress a final report with a detailed statement of findings, recommendations, and lessons learned.