Impeachment is not a legal process, it is a political process

Literally says this in the Constitution.

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.

— Article I, Section 3, Clause 7 paragraph 1 US Constitution.

And this extends from historical basis that in days of yore political power was granted from a liege to a vassal on fief. But there existed the ability for political power to be withdrawn, a person struck from their liege's court, and that would in turn automatically have them lose any title to their fief. That is a loss of political power could also mean a complete loss of your way of life.

The US wanted a clear barrier between political career and personal liberty. This is why Santos is still a free man even though he got kicked out of the House (though that might change soon enough). The two are different processes and they mean different things. Just like if Trump goes to jail but hasn't been disqualified, he's entirely able to run for office.