Lawyers for Eliyahu Weinstein were faced with a difficult situation. After their client’s 24-year sentence for investment fraud was commuted by President Trump in his first term, Mr. Weinstein was charged again with a similar crime by federal prosecutors in New Jersey and convicted at trial in late March.

But his lawyers had a plan. They reached out to the state’s newly installed U.S. attorney, Alina Habba, hoping to persuade her to push for an unusually light penalty, even though their client was a repeat felon.

Ms. Habba granted them a rare private meeting to discuss the sentencing, which is scheduled for September, and she did not invite the prosecutors who had handled Mr. Weinstein’s case, according to two people with knowledge of the matter. The episode left members of her staff infuriated.

A brash media personality and former personal lawyer to Mr. Trump, Ms. Habba is among the most high-profile of the new U.S. attorneys appointed by a president who has taken closer control of the Justice Department than any other in the past half century. She has made frequent media appearances and drawn attention for a series of notable investigations into Democratic political figures.

Her tenure has also shattered morale inside the U.S. attorney’s office and left many prosecutors looking for a way out, according to 16 close observers of the office who were interviewed for this article and spoke on the condition of anonymity for fear of retribution.

Ms. Habba boasted, upon taking office, of her direct line to the White House, according to people with knowledge of her remarks, even as she has insisted that she is “not political.” Prosecutors have chafed at her availability to defense lawyers. She disbanded the office’s Civil Rights Division and killed the office’s longest-running prosecution just days before it was scheduled to go to trial. Three framed pictures of herself now hang in a conference room named for a legendary New Jersey crime fighter, Frederick B. Lacey.