Insights into Curry's Paradox?

Hi, I am trying to more precisely understand some ideas in mathematical logic and find myself drowning a bit in self referential formal logic and theorems by Lob, Tarski, Kripke, Godel... Looking at Curry's Paradox: 1) Let F be: "if this sentence is true then Santa exists" 2) Assume F is true. 3) Since F says “if F is true then Santa exists” and we have assumed F is true, Santa exists. 4) This proves F implies Santa exists; precisely F. So Santa exists by step 3. It is obvious to me that the pathology is self reference (roughly the truth value of the sentence is a different kind of thing then the truth value within the sentence) but how would you be more precise? I'm also interested in being more precise about self reference, godel, strange loops, systems trying to "escape" systems. They too often blend together as concepts in my mind when I think about, e.g., LLMs interpreting their own sparse autoencoders. Discuss