First of all, your original image is in JPEG format, not PNG
This image has dimension 3264 x 2448 pixels with 72 dpi and 24bpp, i.e. about 45.33 x 34 inches. Uncompressed size of this image is about 23.9 MB.
When you open this image with the editor, it creates PDF document with such page dimension and adds this image using ZIP compression to prevent data loss.
And this PDF has about 13 MB due to ZIP compression.
To have a control over compression of the image during conversion you can use New Document -> From Images...
With default settings for compression with your image, created PDF file will have just about 700KB, because JPEG but not ZIP compression will be used.
Now about exporting to PNG.
When you export to PNG with 150 dpi, 32bpp, you will got an image with dimension 6800 x 5100 pixels, and its uncompressed size is 138.7 MB.
So 37.5MB in PNG is not so bad