Is there a modern warship that performs battlecruiser-like flag-showing and power-projection duties?
Short answerThe Zumwalt class comes closest in potential, chiefly as a conspicuous presence ship with concentrated capabilities rather than as a literal battlecruiser.
NotesThe Zumwalt class is the closest potential modern analogue for a ship that can show the flag and project impressive power without being a full carrier. This is a cautious comparison rather than a claim that the class is literally a battlecruiser. Its size and unusual appearance give it diplomatic presence, while its intended weapons and sensors promise concentrated combat power. The resemblance lies in strategic effect and public presence more than in copying an interwar design formula.