This is not actually a problem; after hitting save enough it eventually worked. I have Tableau Public.
I have attached several pictures that show I do not have an extract button in several places. I had the battery-shaped icon before failing to save and after it saved. Why is this missing in mine?
Screenshot 66 shows the "double battery", or more precisely the "double database" icon for the datasource - this means it's an extract in Tableau.
Because you're using Tableau Public you have to use an extract.
Here's Tableau Desktop with a datasource showing that I can extract the data if I want but in Tableau Public it's always an extract, you don't have a choice: