The chatbox is way too high in the rendering z-order of the website, so things like LanguageTool spelling window is displayed behind it:

Apparently, it is forced in fusion css:
.chatbro_container .chatbro_movable_chat {
    z-index: 2147483647 !important;
}

But it has another css with a different z-order that works, but is overridden:
chatbro_container .chatbro_movable_chat {
    position: fixed;
    z-index: 4999;
}

So I have changed that myself to avoid problems with the ads:
Affichage de chatbox minified par-dessus la publicité (z-order max = 2147483647)

ympb_target z-order is 2147483547, but it is dynamically forced to that number and can't be changed (I tried everything).