Saddle height is measured from the center of the crank to the top of the saddle, along the centerline of the seat tube. The vertical measurements that you made do have value. One easy way to measure saddle to bar drop is to measure vertically from the floor to the top of the saddle in the area where your sitbones rest, then measure vertically from the floor to the top of the bars. The difference is saddle to bar drop. Yours is about 5cm, which is fine, for a beginner.

Many fitters will position the saddle fore/aft position so the knee is directly over the pedal spindle. That's OK too, as a starting point, but if you feel too much weight on your hands, try a little further back.

Your stem is probably flipped up. Depending on the angle, flipping it down could lower the bars 2-3.5cm. It will also increase the reach by about 1cm. If you don't find the extra drop and reach to be uncomfortable, go for it. It's the first step toward a racier position.