After thinking for 128 seconds and going through a very similar loop, DeepSeek eventually manages to get out and come up with this

The NFL team whose name doesn’t end with the letter “s” is the Washington Football Team, which was the temporary name used by the franchise from 2020 to 2022 before becoming the Washington Commanders. The name “Washington Football Team” ends with “m” in “Team,” not “s.” This is the only exception in recent NFL history, as all other current and historical team names end with “s.”