You can use Rigidbody in a kinematic sense, and have two kinematic Rigidbody objects detect each other, but you will need to move your objects using the Rigidbody.MovePosition/MoveRotation functions in FixedUpdate, instead of using the Transform.position/rotation properties directly. You already did set your physics to “All Contact Pairs” which is also necessary.
In this diagram, you’re trying to “Move by Transform” but you should switch to “Move by Kinematic Rigidbody.”