Steering wheel still shaking after tire balance

Until you replace that bent rim all bets are off. Vibrations propogate (travel) through matter, and they can come out in unexpected spots.

There’s a second thought that comes to mind. Does it brake smoothly? You could have warped rotors.

If neither of these ideas pan out, ask the tire shop if they can spin the wheels on a “road force balancer”. That would pick up a tire imperfection that normal balancing machines would miss.