Gnome software should try to download icons if they cannot be found from some cache
Fedora 36, gnome-software-42.3-1.fc36.x86_64
In the list of search results, both emoji-picker and ibus-typing-booster show an icon:
But when opening the pages for emoji-picker and ibus-typing-booster, only the emoji-picker page shows an icon, the ibus-typing-booster page shows a replacement picture: