You may be experiencing a bug. As was previously stated, the Chrome badge is added to bookmark icons. So you know it is not a PWA.

This can happen even if the Play Store is unreachable, even if everything is copasetic on the server, the client, the manifest and the website. "Unreachable" includes there being no signed-in user. For mysterious reasons, Play Store access is needed currently to install a PWA.

You can weigh in on this. A bug report has been filed at https://issues.chromium.org/issues/372866273. I encourage all readers to make their way over and vote for it.

We really care because our users are often in places where the Play Store is almost unreachable. Our users give up before the http transaction with the Play Store times out. This, even though the web server is right next door.