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The bug here is that the button is still there when you go back to the first province. The toggle button shouldn't be there if there is no Great Work in the province (as there is nothing to toggle).
Looked into the issue now.
The issue with the button staying I had already fixed so that should be in the upcoming patch.
The issue with the button becoming misplaced is due to The Reaper's Due not being active as that DLC changes how the extended province view looks.
I've fixed that issue as well but can't guarantee that the fix will be in the upcoming patch and might instead be in the next one.
And to be clear with how it works; only provinces that have a Great Work will have the big display in the province view.
for building new ones, the Great Work button next to "Raise Fleet" should be used.
Thanks for the report, it had a lot of details and the .gif made it easy for me to know that i reproduced the issue correctly