Where is the note PDF actually saved on my computer?

Two separate places. (1) The app keeps a private, encrypted working copy of every note it has fetched inside its own hidden support folder (~/Library/Application Support/supernote-todo-desktop/notes/). This cache powers the instant preview, is scrambled at rest so other apps can't read your handwriting, and you don't manage it by hand. (2) A plain, readable PDF copy is written to ~/Documents/Supernote only when you push a note-linked task to a third-party app — that's the copy the task's link points at. So: previewing = hidden encrypted cache; pushing = readable copy in Documents/Supernote.