Over the course of three hours on Tuesday, President Trump scolded Israel and Iran with expletive-laced comments on the South Lawn of the White House. He told reporters he had just chastised the prime minister of Israel, and he shared a screenshot of a private text from the NATO secretary general on social media.

Most presidents deal with international crises in private — at most, they might release a carefully crafted statement.

That has never been Mr. Trump’s style. With this president, the entire world gets a view into his thoughts, gripes and whims in ways that are often reminiscent of a chronically online millennial. His posts come at all hours of the day and night — many self-congratulatory, some trivial, some angry — and his in-real-life appearances can sometimes echo his online persona.

All are windows into his psyche, a trove of insight into the intentions, moods and vulnerabilities of the commander in chief.

To Mr. Trump’s aides, his long-established proclivity for sharing makes him the “most transparent and accessible president” in American history.

“One of the many reasons the president was re-elected is because of his transparency and tell-it-like-it-is attitude,” said Karoline Leavitt, the White House press secretary. “It’s refreshing to the American people to have a president who always speaks his mind and lets the country know exactly where he stands.”