Mr. Ogles, a two-term congressman, had held off primary threats before, despite controversy. But on Thursday, Charlie Hatcher, a former state agriculture commissioner, delivered an upset.

The penalty, imposed by a state judge, is on top of a $375 million fine ordered by a jury that found Meta misled users about the safety of its platforms.

The constitutional right against self-incrimination has been invoked on several occasions during high-profile — and contentious — hearings.