The litmus test for whether a State's districts are representative (i.e. 'fair') is simple: do the number of representatives from each party roughly match votes cast?
Sure, for the House. Looking at the math on national scale, they look pretty good. In this election democrats got about 52% of the vote, and they will hold about 52% of the seats. It's close, on a national scale.
Except the only relevant scale for House races is at the State level. Why? Because each State sets its own districts, and no state can influence the votes of another state.
The Senate is an entirely different level of fucked up, which I realize is by design. 57% of Americans voted for a democratic senate candidate, and yet democrats will only hold 44% of senate seats in the coming congress. That's a 13 point spread! I don't think anyone argues that state lines are gerrymandered on purpose, but they are indisputably inefficient at representing the country and they definitely give a large advantage to one party. Some of our more stubborn founding fathers made absolutely certain that rural people would have a deliberately disproportionate voice in our government, and we are suffering for their ignorance to this day.
The Senate has its own quarks, but it isn't due to Gerrymandering. By definition you can't gerrymander a senate race, because the entire state gets to vote for one candidate, and for all states except Maine whomever gets the most votes wins.
But you've highlighted the inherent unfairness with the US Senate - we've got California with ~39MM people and two Senators, and then we've got about 19 states that combined have fewer people but collectively have 38 senators. With the odd exception of tiny Rhode Island these are extremely rural states, which means rural voters and rural issues are grossly overrepresented in the Senate. The GOP has held power by appealing to rural voters who are a minority in this country (~19% US citizens live in rural areas) but hold a huge amount of political power.
AS you said, it was by design, but not what the founders envisioned. In 1800, shortly after 'the great compromise' was struck, only about 8% of people lived in urban areas. Now it's about 80%.
*Maine uses ranked-choice voting for federal elections.