“The Presidential election has nothing to do with any election for Senate, aside from being held on the same day.”
The language of Article I Section 5 refers to the person and not to the potential office:
“Each house shall be the judge of the elections, returns and qualifications of its own members....”
Normally, that language makes no difference and has the effect you desire, but when a sitting senator is trying to become Vice President or President, the language of Article I Section 5 has an effect you apparently don’t desire.
But the Senate is designated at Selecting the VP if the election is tossed to Congress. So, they ARE responsible for “electing” Harris if it is sent that way.
I am sorry but your arguments about the Natural Born clause were dismissed in a “de facto” manner when Obama was elected.
The States have their own rules and they determined she was eligible. Although most states, by statute have to “testify” that their nominees are eligible. I don’t think the states even “research” candidates about how long they’ve lived in the US.