What is the difference between
Also is checking if
Paid a valid way to see if the user’s payment has successfully gone through?
campaign_pledge_amount_cents is in your campaign’s currency. That is what you should be using to determine whether the patron’s pledge in respect to your currency. Especially if you already have an existing integration/app.
patron_status and last_charge_status are good fields to use. However using campaign_pledge_amount_cents should be enough.