Your formal rendering of this as
~p -> p is misleading. This looks like a statement in FOL (first order logic). But first order logic specifically forbids self-referential statements. That was necessary in order to create a system where all statements are decidable. So in FOL, p cannot refer to "this sentence." Second order logic is more powerful, but it too is set up to avoid self-reference. In general any logic that admits self-reference is vulnerable to paradox. So this statement cannot be accurately rendered in a formal logic system.
So let's set aside the formal rendering entirely. Is this a natural language paradox (meaning it cannot be unambiguously true or false)? Let's see if can be true. "If this sentence is false, it is true." We're assuming it's true, so the condition is not met, so the consequent can be either true or false. So there's no contradiction or paradox here.
Now, can it be false? If it is false, then the condition is true, which means the consequent is true, which is a contradiction. So that implies this sentence is vacuously or tautologically true, at least as determined by informal logic. We are in a system that allows paradoxes, but this is not one.
(Note: As of October 2023, ChatGPT does not analyze arguments logically, it uses context clues to guess at an appropriate response. Since this "looks like" a paradox, ChatGPT classifies it as one, inaccurately.)