Favicon does not appear in the manifest

Humm. Here’s the logic for obtaining the icons:

https://github.com/GoogleChromeLabs/pwa-wp/blob/30ee437e581c69bd3f771fc3012517d1f6a151b8/wp-includes/class-wp-web-app-manifest.php#L485-L524

I would investigate whether get_site_icon_url() is returning what you expect.