Not sure that Bridge of Spies qualifies as the second Spielberg film not scored by John Williams. Duel was feature length and released in cinemas so it surely qualifies. (And arguably the feature length TV episode LA 2017 does too. Though I'd definitely discount his amateur feature length film Firelight).
Fair point, but Sugarland Express is considered his feature film debut since Duel was made for TV and only re-edited to be released in cinema. For posterity, it is consistently referred to as a TV movie.