In the pre-Trump era, indictments and investigations by federal law enforcement could have been fatal to a Republican campaign. But Mr. Trump has instilled a deep mistrust in government institutions like the F.B.I. Mr. Paxton took the unusual step of authorizing an investigation of an F.B.I. investigation — he appointed a special prosecutor to look into the federal probe of the wealthy donor, an Austin real estate investor named Nate Paul whose home and offices were raided by federal agents.

The litany of allegations against Mr. Trump has allowed acolytes like Mr. Paxton to claim that they, too, are victims of a government conspiracy.

“That’s the Biden F.B.I., the Biden D.O.J.,” Mr. Paxton said in a recent interview with a Fox News reporter. “They were under investigation by my office. I don’t know what they are going to do. All I can tell you is that we were doing the right thing. We are going to continue to do the right thing. I don’t control what the Biden White House does.”