The sentencing of one former ally of President Trump and the disclosure of a key agreement with another intensified the focus on Mr. Trump’s alleged role in coordinating efforts to suppress the stories of two women to protect his 2016 campaign.

The dual developments on Wednesday came as part of a legal saga that has led Mr. Trump’s own Justice Department to directly implicate him in federal crimes, exposing him to potential legal and political peril as he enters the second half of his presidential term.

Michael...