Yes, "new math" is neither magical nor unrelated to existing math, but that doesn't mean any new theorem or proof is automatically "new math." I think the term is usually reserved for the definition of a new kind of mathematical object, about which you prove theorems relating it to existing math, which then allows you to construct qualitatively new proofs by transforming statements into the language of your new kind of object and back.

I think eventually LLMs will also be used as part of systems that come up with new, broadly useful definitions, but we're not there yet.