Payment page: not a modal. The user might want to add more stuff to the cart, even when they are literally one click away from purchasing. Blanking out the rest of the page means they now have to work around the site to buy more stuff.
Error message: not a modal. The user is vanishingly unlikely to report an error immediately (obviously it's logged in any case), and probably just wants to try again with slightly different input.
Irreversible action confirmation: not a modal. For the same reason as the payment page, the user might want to do something else before retrying the irreversible action. Just display a prominent message so the user knows the action is not yet done. Or, if at all possible, implement undo instead.
My job depends on it: OK, use a modal. We forgive you.