Did you read the last sentence of the post I linked? Laurelorn is not treated as being part of Ulthuan officially or unofficially. While that last sentence might have been discarded because whether humans are banned from Ulthuan
might have been invented by the fandom rather than GW, it indicates that Ulthuan's official policy towards Laurelorn is to treat like... not Ulthuan. If Ulthuan's policy was to treat Laurelorn as independent in fact only, Boney would not have said that they were only allowed to dock at Lothern.
The simplest explanation to this is that Mathilde made a mistake. Mathilde said nothing about "it puts it into agreements with other nations." She said that it recognizes it wholesale. Just flat out and unmodified. Mathilde would not have said it would have huge ramifications on Laurelorn and Ulthuan's relations if she had known Ulthuan already recognized Laurelorn's independence. She would have said something like what you said. That putting it into words with nations like the Empire and Kislev would be significant. Not that the action in and of itself would be significant.
Again, the simplest explanation here is that Mathilde made a mistake.