How do I convert a 3-axis quaternion to a 1-axis x-y axis plane?

The MPU6050 has no yaw reference
you need a magnetometer

I only care about relative yaw and I don't care where north is. I will zero out my rotation/position when the robot boots up and then just use relative rotation/position from there. This is just a toy.

My main need for rotation is to be able to go in a straight line. It only has two wheels and right now it wanders drunkenly because the motors don't perform the same even when given the same voltage. This make driving hard. I did not anticipate this in the initial design although I should have. A four-wheel vehicle with all wheels straight doesn't have this problem.

I will use feedback from the 6050 to adjust voltage to the motors. With my planned simple transformation it will only work on a flat floor. If it goes up a ramp the driver will have to compensate although that will be rare.