“I thought so, too, but that is not true.
Article I, Section 3:
Judgment in Cases of Impeachment 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 Punishment, according to Law.”
Due process.
Alcee Hastings aka “Corruption wearing shoes” was removed from the bench by impeachment.
However since he was not convicted by a court of law he could not be disqualified from office.
Which is why he held office in the US House after being impeached and convicted.
A not guilty judgement by a federal court would obviate any disqualification imposed by congress.
Thomas Porteous, a federal judge from Louisiana, was convicted in 2010 on 4 counts, removed from office, and disqualified from Federal office by a Senate vote of 94-2.
Look it up.