Correct. The Senate was designed torepresent the states, by which the Constitution meant the legislatures of the states, since according to the republican ideology of the time, legislatures were the dominant over executive and judiciary. In most states, that remains the case. In Texas, for instance, the lieutenant government—the presiding officer of the Senate—has more real power than the governor.
I long for the day when the 17th is repealed and the states take back what they freaking gave away 96 years ago. I sometimes wonder what was so “progressive” about them back then.