Its long time ago that support of Overleaf has worked. I wrote already a letter to Overleaf and to you (LanguageTool) — and both says: “please contact Overleaf→LanguageTool; LanguageTool→Overleaf”.
Maybe you can contact them by self and try to integrate your service? I think it’s a win-win situation!
That’s strange, as it works with all the documents I have tested with (at least the icon shows up). Could you share a link to the document for me to reproduce the problem?
I see the issue now: our add-on activates itself on overleaf.com, but you’re using an Overleaf instance on a different domain. We’ll see if we can fix that in a future release.