I wonder if this is possible because
apk is a compressed archive which can't capture this information while being downloaded. Is it possible that google play store and google play services maybe adding this information after you install that apk.
Most of the time I don't even download or update apps from play store in my every android phone. I just share the apk from one device among every other home device via wifi and side-load them. How do they come to know the download source in this case?