There is nothing wrong. The booster diaphragm is evacuated on both sides by the vacuum from engine manifold. When you apply brakes, a valve is shut to back of diaphragm and the vacuum is bled off the back side of diaphragm so the vaccum pulls (or more correctly the atmospheric pressure on back side pushes) the diaphragm forward to help you apply pushrod into back of master cylinder. When you pump brakes the vacumm has to be replenished rapidly and the volume is enough that it constitutes a large vac leak on a 4 cyl engine.

If you do this on a big cu inch V8 the volume is much smaller compared to engine air needs at idle so the flow from this makes little difference.

The booster test is to turn off engine and push pedal several times to bleed out all vacuum. Start engine with foot on pedal and see this it drops an inch +/-.

That sounds 100% normal. When the brake pedal is up, there's engine vacuum on both side of the brake booster diaphragm. When you apply the pedal, atmospheric pressure (air) is metered into the backside of the diaphragm to create an imbalance, causing pedal assist (pressure boost, hence the name booster). As soon as you release the pedal, that air is drawn into the intake manifold. Pumping the brake is exactly the same thing as creating a pulsed vacuum leak...and more air is basically a larger throttle.

Try the same test with a Chevy or a Hyundai, you'll get the same result.

You might put a vacuum gauge on the vacuum line to the brake booster to pin down what is happening. There is a check valve on the booster that can fail.