Steering wheel shakes when brakes are applied lightly

Sounds like a warped break rotor. Needs breaks.

The better question is, "why are the rotors warped?" replacing them without figuring out why will only cause the new rotors to warp again.

look for a caliper that is dragging if only one rotor is found warped. a caliper that is found to not be retracting one or both pads on one side will cause extreme heat to the rotor at speed. if both are found warped, check both calipers. be sure to also check if the brake cooling ducts are obstructed.

when replacing the rotors, be sure to replace the brake pads also AND the brake sensor wire. don't use old pads with new rotors and vice-versa.

This is caused bt warped disc brake rotors, they can be refinished or replaced, it depends on how bad they are out of true.