I just discovered that to display your favicon in Google and Bing search results, it should be an ICO with type image/x-icon
In <head> add an ICO
<link rel="shortcut icon" href="https://example.com/images/bookmark-icon.ico" type="image/x-icon">
…in addition to the standard icon file
<link rel="icon" href="https://example.com/images/bookmark-icon.png" type="image/png">
… and the icon will show up next to search results.
