WASHINGTON—Top U.S. national security officials will see how the failed war in Afghanistan may be reshaping America’s relationships in the Middle East as they meet with key allies in the Persian Gulf and Europe this week. Secretary of State Antony Blinken and Defense Secretary Lloyd Austin are traveling to the Gulf separately, leaving Sunday. They will talk with leaders who are central to U.S. efforts to prevent a resurgence of extremist threats in Afghanistan, some of whom were partners in the 20-year fight against the Taliban. Together, the Austin and Blinken trips are meant to reassure Gulf allies that President Joe Biden’s decision to end the U.S. war in Afghanistan in order to focus more on other security challenges like China and Russia does not foretell an abandonment of U.S. partners in the Middle East. The U.S. military has had a presence in the Gulf for decades, including the Navy’s …