After some rough testing, it turns out that fennec does request wallpaper data on gitlab every time it is networked, which does explain the cookie.
The reason why Mull is mentioned is because it was still being maintained when this gitlab issue was filed, except that the issue went unanswered.
It wasn’t until recently that I was reminded that I could ask a question in the forums, so I lazily copied the original issue here, but I’ve long since abandoned Mull.