The same place as it stores the data to show the forecast on the dashboard or the entity more info dialog. I do not know where that is, but it doesn’t use an API call to request a new forecast every time you open your dashboard.
My previous comment is based on the information shared at the time the attribute was removed. I don’t have the background knowledge to explain how it works.
Here’s an example: [PETITION] Don't delete the forecast attribute - #27 by petro