This is what we get if we try to make the background look in full size on small screens:

https://wpforo.com/wp-content/uploads/2022/10/wpforo-background-img.jpg

I have set the minimum screen size, when the IMG size is not changed, smaller max-width would crop the IMG.  

@media (max-width: 540px) {
  #wpforo #wpforo-wrap .wpfl-2 .wpforo-category {
    background-size: contain !important;
  }
}

In that case, the top and bottom parts would stay empty, as you have used wide IMG.

I would like to try if it was possible

In that case, the top and bottom parts would stay empty, as you have used wide IMG.

Here is my recommendation: https://wpforo.com/community/postid/72283/