Is PWA Support Really Worse on Android 13 and Later?

I've noticed that after upgrading to Android 13 and now with 14 and 15, the experience with Progressive Web Apps (PWAs) has changed. In Android 12, when users clicked to install a PWA, it installed directly, blending seamlessly with native apps. But now, on Android 13 and higher, there's a second prompt that says 'Add to Home screen'. This is a bit annoying because the installed app ends up showing a Chrome icon on the bottom right corner. I've tested this across various smartphone brands and it's consistently the same issue. Is there any way to fix this?