Interesting. Thanks.
The action of the house seems kind of irrelevant. 2/3 of the senate can convict a senator after impeachment by the house, or 2/3 of the senate can expel a senator with no action by the house.
It’s also important to remember that in 1798 Senators were appointed by their state legislatures and not directly elected. But I think the point was that they realized that the impeachment process was useless because they couldn’t do anything other than remove him from office which they had the power to do by themselves anyway.