I am working on my website. I managed to get basic PWA functionality using the web page manifest file.
Not long ago, Google released deeply integrated PWAs, allowing use
This is not something we can control. Chrome was/is experimenting with "improved A2HS" as they called it (A2HS stands for "add to homescreen") and a part of that was an internal service that wrapped the PWA into APK. It was hidden behind a flag initially, then it was opened to the public as default in Feb 2017.
When you install a Progressive Web App, we look at your Web App Manifest and other meta-data and create the APK that is installed on to the user's device.
(emphasis mine, we == Android)
So there's nothing we can do except being sure our manifest is valid, site is HTTPS, Service Worker installs correctly etc.