for homescreen shortcuts, no icon is displayed in Safari

[Raiden-GH]

The favicon of the DeltaChat website is not displayed in Safari, because the required header may be missing.

[Simon-Laux]

For me favicon is shown, what you mean is probably one of the apple specific PWA icons that you can define (which have higher resolution than the favicon) - I think they were called "apple-touch-icon" or sth similar?

Where exactly in safari is the screenshot from?

[Raiden-GH]

The screenshot is from the Safari home screen in macOS. But the same problem exists in iOS.

I think they were called "apple-touch-icon" or sth similar?

I always thought they were called favicons. ArcaneChat website had the same issue.
According to ADB, a special header for Safari needs to be added.

[Simon-Laux]

I always thought they were called favicons.

there are multiple different icons that you can set (see https://realfavicongenerator.net).

favicon is the oldest and supported everywhere.