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Sorry, but it seems you misunderstood the geometry that is at work here. If it helps, just draw the side view of a bike cockpit on paper and see what happens.
The fork steering axle is running at an angle (HTA). If you lift your grips vertically above that axle, they move away from that axle. That's exactly what a stem is, space between the steering axle and the grips.
And if you lift the grips in parallel with the steering axle, you move the grips towards the rear of the bike. Because the steering axle is tilted towards the back. Which results in shorter reach.
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