I'm the world owner in question.
I also have this problem of "no Manuscript button" on worlds where I am any status other than "Owner".
When I checked at
C. B. Ash's request, I saw that I do have the Manuscript button as the 5th one down:
When I then checked worlds where I am not the Owner -- I am Co-Owner, or an Advanced Editor -- I was able to confirm the lack of button a few times. It did not matter if I was activating a Campaign, or a world where no Campaign exists.
Edit: The below weirdness has resolved itself. Left here in case the occurrence was part of the total bug process.
And then I got this:
which is being included here in case it is relevant to your analysis.
It's also now the only thing I can see on World Anvil other than the Bug Tracker.
I can't even log out.
Which is why I'm having to host my illustrations of the bug, in hopes that it helps your reproduction of same, openly somewhere else on the internet. Please tell the original poster, Inner Sanctum member Kummer Wolfe, when you no longer need my images so I can delete them.