“Per the constitution, the Senators represent the states while the Reps represent the people”, not after the 17th Amendment was passed.
The fundemental definition didn't change. The intent was subverted by the 17th Amenedment. So, I agree, you are correct in application. The state legislatures no longer pick their senators. The 17th made the people pick them and thus function about the same as house reps except with much less accountability.
There is no doubt that if Senators had to answer to Governors and could be replaced by state legislatures, they would behave and legislate much differently.
The 17th Amendment may actually be the most damaging thing we have ever done in that it moved power from the states to the Fed by accidentally removing the Senators accountability. Term limits wouldn't be discussed if Senators had to deal with Governors.