Hi, have you by any chance checked the Cursor Docu or Privacy pages?
The cursor team has answered this in very recent threads as well. This one is old and wont be updated, more recent ones have your question answered.
They also posted details in their Docu pages:
And
But other docu pages have also more on privacy related, you can search in docu by keyword.
In short: The models run on 3rd party AI providers and those providers privacy policy applies for anything not listed in the above 2 pages.