Jumping with rigid body3d

Scientific notation means that the value of y too little. And the character jumps badly because of this line of code:

 playerRigidbody.velocity = new Vector3 (forward.x, 0, forward.z) .normalized * movementVelocity;

Here you reset velocity.y, so the jumps are low and the fall is slow :)

Instead of the line above, write the following:

 var velocity = new Vector3 (forward.x, 0, forward.z) .normalized * movementVelocity;
 velocity.y = playerRigidbody.velocity.y;
 playerRigidbody.velocity = velocity;