The chop of U.S. military helicopters whisking American diplomats to Kabul’s airport on Sunday punctuated a frantic rush by thousands of other foreigners and Afghans to flee to safety as well, as a stunningly swift Taliban takeover reached Afghanistan’s capital. U.S. reports of gunfire at the airport threatened to shut down one of the last avenues of escape in an ever-more chaotic and compressed evacuation. NATO allies that had pulled out their forces ahead of the Biden administration’s intended Aug. 31 withdrawal deadline were rushing troops back in this weekend to airlift their citizens, while the Pentagon was sending in...