The top third of my home screen icon is chopped off now with iOS13.
Though when I tap on the icon to open my web app, then hit the home button to return to the home screen, my icon is shown in its entirety for a brief moment. Then the top third of it disappears.
I’d start with fixing that and seeing if there is anything else. For example, it looks like you are only deploying images/calcrimes.png (304x90), with no other sizes.
Let us know what you find - others could be having similar issues!