A few weeks after winning the election, President-elect Donald J. Trump found himself face-to-face with Gov. Wes Moore of Maryland, a rising star in the Democratic Party, as the two men made their way through the bowels of Northwest Stadium in Landover, Md., to watch the annual Army-Navy game.

The governor greeted him effusively.

“Mr. President, welcome back to Maryland, sir, welcome back to Maryland!” Mr. Moore said. “Great to see you, great to see you, great to have you back here.”

“You’re a good-looking guy,” Mr. Trump observed.

“We are very, very anxious to be able to work closely with you,” the governor added. Then he mentioned the ongoing efforts to rebuild the Francis Scott Key Bridge outside Baltimore, which had collapsed that March.

This chummy encounter was captured on camera for a documentary series called “Art of the Surge,” now streaming on Fox Nation, which provides a rare behind-the-scenes look at the adulatory environment in which Mr. Trump has moved since regaining power. The series gives a sense of how much he is enveloped by people eager to stroke his ego and get in his good graces — including some unexpected figures, according to advance episodes viewed by The New York Times.

At one point, inside the V.I.P. box at the football game, Brian Grazer, a top Hollywood producer, gets his photo taken with the president-elect and confides to those in the room that he cast his ballot for the Republican.