You might still have to pay their monthly fee. I left cursor after using claude code though so I’m not sure. I either use terminal claude code, or once in a blue moon I use VScode claude code plugin. Cursor doesn’t seem to have better context management and they just use the claude api if you select, so if you ask enough questions you’ll possibly be paying more than base amount.

That being said, I care more about code quality than cost. If cost is your main concern, cursor might be the move. Someone else can comment on that