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Extremely short version

Instead of serving dozens of icons, all you need is just five icons and one JSON file.

In your HTML, for the browser:

<link rel="icon" href="/favicon.ico" /><!-- 32×32 -->
<link rel="icon" href="/icon.svg" type="image/svg+xml" sizes="any" />
<link rel="apple-touch-icon" href="/apple.png" /><!-- 180×180 -->
<link rel="manifest" href="/manifest.webmanifest" />

And in your web app manifest:

// manifest.webmanifest
{
"icons": [
{ "src": "/192.png", "type": "image/png", "sizes": "192x192" },
{ "src": "/512.png", "type": "image/png", "sizes": "512x512" }
]
}