To that point, Mr. Murdoch’s publicists — who declined to comment for this article — conspicuously confirmed rumors last month that the mogul did not expect Mr. Trump to recapture the presidency. And several people who have worked with Mr. Murdoch said he harbored no malice toward Mr. Biden and had even expressed some admiration of the former vice president on occasion.

It would not be the first time Mr. Murdoch has stayed loose to maintain influence with whoever comes into power. In England, he became an ally of the Labour prime minister Tony Blair, despite years of backing Tory rule. The Biden administration is likely to handle regulatory disputes that could affect Mr. Murdoch’s domestic assets, which include sports and entertainment networks as well as Fox News, The Journal, and The Post…

Some prime-time personnel, protective of their ratings success, were unnerved after seeing some viewers turn against the network after the Arizona call; one group of protesters chanted “Fox News sucks!” outside a tabulation center in Phoenix.

On Monday, Mr. Hannity and Mr. Carlson stoked Mr. Trump’s shadowy narrative of a suspicious election. “The Washington swamp, Joe Biden, all desperate, they want to just call it a day and stop you from asking legitimate, tough questions about the election,” Mr. Hannity thundered to viewers.