But we need to be crystal clear, here. Not sentenced by the Senate does not remove the fact that the subject was Impeached. Is the bar against holding future office contained within the Impeachment itself (by the House) or is it a sentencing option available to the Senate?
It is not an option. It is a specific penalty under the Constitution -- but it applies only if the Senate renders a guilty verdict.
The Constitution, Article I, Section 3:
The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present.Judgment in Cases of Impeachments shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust, or Profit under the United States, but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment, and Punishmnet, according to Law.