My favicon appears in browsers, appears when added to iOS home screens, appears when added Android home screens, but when I try to “Add to Favorites” in iOS, the icon does not appear. It won’t appear in the favorites screen either. I tried the just using customizer to add an icon file. I tried using the plugin Favicon by RealFaviconGenerator to add it, and while that gave me a lot more Favicon options for various devices, it did not fix the issue.
I don’t really have enough experience with iOS icons to know why that wouldn’t be working. The site icon feature is a core WP feature, so you might have more luck asking over in the WordPress.org forums – they might have seen this issue before and know the fix.