I don't think that this delays anything.
First, F$U has already requested that document within the existing lawsuit. And they might not "need" the document to prove most of their arguments.
Second, this is a bit broader, on "public policy" grounds. Meaning, let's say that F$U gets the contract in the lawsuit, it might still be redacted or subject to usage ONLY within the lawsuit, while the Florida AG is saying "hey, if you do a contract with a state institution, that document should be public".
What is funny about this is that becomes another bite at the apple. Even if a NC judge says "ESPN contract can remain secret", the Florida argument is a very different one, and a Florida judge may rule very differently.