My '99 Camry V6 has slightly loose steering and a quiver in the wheel when braking. Brakes are in good shape. Would braking accentuate a ball joint, tie rod or strut problem, communicating it to the wheel?
I think you may have two issues.
Tie rod ends end, or other steering/suspension parts maybe worn causing loose steering. This could be dangerous!
Brake rotors maybe warped causing the steering wheel shimmy when braking.
Came across one in the recent past and the “U” clamp that holds the RH end of the steering rack to the frame had come loose. one fastner missing completely and the other about the fall off.
Check your rack is tied down OK.