You're an "expert in image processing" but don't understand the fundamental difference between the .jpg and .png image formats or the encoding and compression algorithms underpinning them? I find that doubtful.

.png only compresses efficiently when used as intended, which is for screenshots or other images with large areas of solid colors, where each pixel is most likely the same color value as its neighbors. In this use case, it's much more efficient than .jpg. However, .jpg is much more efficient than .png when it's used as it's intended; encoding images of the real world, like images taken with a digital camera, where each pixel has a slightly different color value than the ones next to it.

You can test this yourself by taking a picture with your phone's camera, then copying the image, converting the copy to the other file format, then comparing the file sizes. Next, repeat the process with a screenshot of a web page or a simple Paint drawing. You'll see that the camera image is smaller as a .jpg but the screenshot is smaller as a .png.