Image in the search box

Sure! The search box is a custom HTML sidebar widget, correct? Insert appropriate <img> tag HTML where ever you like within the <form> ... </form> elements.

it’s a short code…

I made another widget with a picture, is it possible to eliminate the distance between this widget and the search and filter box? https://test.sacconicase.com/

section#media_image-6 {
    top: 6px;
    margin: 0;
    width: 95%;
    position: relative;
}

You can specify border radii for each individual corner so the two widgets could appear as one. For the image, only radius the top corners:
border-radius: 10px 10px 0 0;
Do the reverse for the form’s corners.