“Because of his incredible Success & Comeback in Sports (Golf) and, more importantly, LIFE, I will be presenting him with the PRESIDENTIAL MEDAL OF FREEDOM!” Mr. Trump wrote.

Mr. Trump’s allies and advisers see his use of information flow, particularly on Twitter, as one of his strengths. He presents himself to supporters not just as an elected official representing them, but also as a source they can believe.

“Part of the reason that the president was elected in the first place was because he reflected the distrust and disdain that large swaths of the country have had for the mainstream media for many years now,” said Andy Surabian, a Republican strategist and a former special assistant to the president in the White House.

Boris Epshteyn, now the chief political commentator at Sinclair Broadcast Group who also served as a special assistant to Mr. Trump, said the president had “consistently been very effective” at dealing with the media during his career, and that as president, he had “the most powerful loudspeaker in the world, both through traditional and social media channels.”

For all of the mystery surrounding Mr. Trump’s uses of his unscheduled hours, some aides privately concede that a large portion of that time is spent with a television on in the background. When he eats lunch in his dining room with visitors, a TV is usually on, either turned down or muted, until there is something he wants to hear. When he travels on Air Force One, he toggles between the Golf Channel and Fox News. The morning hours blocked off for unstructured executive time are often interspersed with tweets responding to television commentary on Mr. Mueller’s report.

To reinforce Mr. Trump’s view that he has been “exonerated” by the investigation, White House surrogates who appear on cable news in support of the president have received a barrage of emails, many written by Julia Hahn, the White House surrogate liaison, declaring the president fully vindicated.

Democrats have made a point of rejecting the notion that the president should be placing himself at the front and center of every major cultural development. “Starting today, we are going to change the channel,” Pete Buttigieg, the mayor of South Bend, Ind., said in a speech announcing his presidential candidacy on Sunday, adding that it was time to end Mr. Trump’s “horror show” in Washington.