If the senate cannot remove a federal official already out of office, how can they disqualify said person from running for office again? [duplicate]

Question

Background

House Majority Whip James Clyburn has stated that the House may wait until after Biden's 100 days to send articles of impeachment to the senate as reported by CNN:

"We'll take the vote that we should take in the House, and (House Speaker Nancy Pelosi) will make the determination as to when is the best time to get that vote and get the managers appointed and move that legislation over to the Senate," Clyburn told CNN's Jake Tapper on "State of the Union." "It just so happens that if it didn't go over there for 100 days, it could -- let's give President-elect Biden the 100 days he needs to get his agenda off and running, and maybe we'll send the articles sometime after that," the South Carolina Democrat added.

This would seem to render the trial moot, as at that point the officeholder whom the articles were introduced against is no longer holding office. Indeed, one reason being floated around is to deny Donald Trump the benefits of being an ex-president as described in the Former Presidents Act, which states the following:

(f) As used in this section, the term “former President” means a person--

(1) who shall have held the office of President of the United States of America;

(2) whose service in such office shall have terminated other than by removal pursuant to section 4 of article II of the Constitution of the United States of America; and

(3) who does not then currently hold such office.

However.....for point 2, if the trial was held after president Donald Trump left office....then that means his service in office was not terminated by section 4 of article II of the constitution and therefore still qualifies as a former president. Separately (and more to the point of the question), you cannot be disqualified from running for office until after you are removed according to this Politics.SE answer:

7. Following the Verdict of Guilty or Not Guilty, or the Pronouncement of Judgment, and the Disposition of the Disqualification From Holding Office of Trust or Profit, If Presented, the Senate Sitting as a Court of Impeachment Adjourned Sine Die.

However...if the person being impeached is no longer in office, then they cannot be removed from an office they no longer hold. This reality is what prompted me to ask...

Question

If a federal officer cannot be removed from office because their term has already ended, how can the Senate proceed with subsequent punishments related to impeachment as outlined in the constitution?

Answer 1

The vote to bar an individual from holding public office again comes after the vote to convict. As such, even if the vote to convict and remove a President is moot, the subsequent vote to bar the individual from holding public office again is not moot.

This was affirmed in a Senate vote during the trial of Judge West H. Humphreys. The annotated Article II Section IV of the Constitution notes:

The Senate imposed disqualification twice, on Judges Humphreys and Archbald. In the Humphreys trial the Senate determined that the issues of removal and disqualification are divisible, 3 Hinds’ Precedents Of The House Of Representatives § 2397 (1907), and in the Archbald trial the Senate imposed judgment of disqualification by vote of 39 to 35.

During the Senate debate on whether the vote to bar an individual from holding future public office is separate from the vote to convict, Senator O. H. Browning of Illinois argued:

We have the authority of an adjudicated case of the action of the Senate, in which they found a judge guilty upon impeachment and entered against him a judgment of ouster from his office; going no further. I apprehend it was competent for them to do that. They were not bound to attach to it the other consequence that may be attached to it under the Constitution, of disqualification forever thereafter to hold office. It may frequently occur—it occurred in that case, it may occur again—that a majority of the Senators would feel it their duty to vote for his ouster from office, and would not feel it their duty to vote for his disqualification forever thereafter to hold any other office under the Government, however unimportant.

Source: Hinds’ Precedents Of The House Of Representatives § 2397

The judgement was as follows:

In the judgment of the Chair these are separate and divisible propositions. * * * From the authority of the Pickering case the Chair is obliged to say that it is a divisible proposition.

Source: Hinds’ Precedents Of The House Of Representatives § 2397

This Vox Explainer sums it up:

The Constitution is silent on whether, after an official has already been impeached and removed from office, imposing the additional sanction of disqualification requires a supermajority vote. In the past, however, the Senate determined that a simple majority vote is sufficient for disqualification. Judge Archibald was disqualified by a vote of 39-35 after he was removed from office.

To be clear, such a simple majority vote may only take place after the Senate has already voted to convict an impeached official. Two-thirds of the Senate must first agree to remove someone from office before that official can be disqualified — a simple majority cannot, acting on its own, disqualify an official from holding future office.