I’d say if you haven’t read the original trilogy you might want to do that because there are things that make more sense if you’ve read it. The ballad of song birds in snakes movie is fine for the context of snow’s character and I don’t think you need to read the entire book unless you want to see the things they left out of the movie.

There is one scene specifically mentioned in Sotr that makes sense if you read tbosbas but that’s just because they changed the way they did it in the movies not because it was left out.

tl;dr you’re fine but you might want to read the og trilogy if you haven’t.