OMG with the fail facial recognition again.
When the President of the United States is tried, the Chief Justice shall preside
They, the Senate, are judge advocates.
And you forgot the rest of the paragraph:
"The trial of all crimes, except in cases of impeachment, shall be by jury; and such trial shall be held in the state where the said crimes shall have been committed; but when not committed within any state, the trial shall be at such place or places as the Congress may by law have directed."
This refers to the trial of crimes.
So, panel of judges presided by SC Chief.
"The Senate sits as a High Court of Impeachment in which senators consider evidence, hear witnesses, and vote to acquit or convict the impeached official. In the case of presidential impeachment trials, the chief justice of the United States presides."
Which describes a judge(s) and jury…
https://www.senate.gov/artandhistory/history/common/briefing/Senate_Impeachment_Role.htm