Luckily it is not coming from the search plugin. There is this 3rd party CSS rule, which resets the background image on all elements of items which are placed in a container, which have the “e-con” and “e-parent” CSS classes. If I turn them off in the debugger, the issue is gone.
It seems to be related to a lazy loader of some sort.
A custom CSS is not going to help in this case, as overriding the background image will also override the background on the search – you can’t restore what’s overwritten. The CSS rule in the screenshot has to be removed or adjusted, as it overrides the initial color.