She draws much of her influence from her close relationship with Taiwan’s president, Tsai Ing-wen, who represents Taiwan’s pro-independence Democratic Progressive Party, and for whom she once serves as spokeswoman. In addition, Ms. Hsiao counts Mr. Bolton and Mr. Biden’s top National Security Council official for Asia, Kurt Campbell, as decades-long friends.

For years, U.S. officials prohibited Ms. Hsiao’s predecessors from visiting the White House and the State Department. Such guidelines have relaxed over time, and she now pays regular, if discreet, visits to the West Wing and Foggy Bottom.

She is an undisguised regular on Capitol Hill, as when she sat next to Kevin McCarthy, then the House Republican leader, last summer for a livestreamed discussion by his caucus’s China Task Force. “She really does have the confidence of people here in Washington,” said Bonnie Glaser, a China expert with the German Marshall Fund who has also known Ms. Hsiao for many years.

Seated in an elegant reception hall at Twin Oaks, with a grand piano and floor-to-ceiling windows overlooking a rolling lawn, Ms. Hsiao described her position as “legally unofficial.”

For that, she blames Beijing. “The Taiwanese resent not only being bullied, but we resent being told that we cannot have any friends,” she said.

It helps, Ms. Hsiao said, that appreciation in Washington has grown “for Taiwan as a democracy, as a force for good, and as a true partner of the United States.” At the same time, she said, the threat from a Chinese government that talks of absorbing Taiwan weighs heavily.