Software needs to putting shit overtop of whatever is on your screen for anything that doesn't demand immediate attention unless it was deliberately initiated by the user.

I actually like that it gives some indication that you can "install" a site when it has a PWA, but there is no goddamn need to block the main content for that.

There are so many better ways of doing this:

Remove useless fucking home button that functions almost exactly like the "New Tab" button for 95% of users. Then expand the settings icon in the URL bar into an "Install PWA" chip.
Recolor the overflow menu icon to match your system's accent color (or just blue) and put a little alert dot over it. Then have it be the first option in the overflow menu.
Don't overlay the website with a popup, but expand the topbar down, shifting the content window below without obscuring it. Better yet, slide in similarly from the bottom, so it doesn't shift the entire page content down.

This behavior could be reused for any of the things Chromium-based browsers shove in your face. Reader mode, permission requests, download completion notifications, etc. could all use these mechanisms instead of getting in your way. Modern software is so antagonistic to users.