The Chinese room does not aim to show, nor does it show, that part-whole relationships fail nor is it even about part-whole relationships.
Yes, neurones do not understand "pen" -- but some highly particular whole bodies do (ie., english spekaing people). That's because of highly particular relationships between those neurones, the body, the environment, and the history of that language user.
This is the csci brain rot that searle is baffled by. Symbol manipulation implies no relationships between wholes and parts. The capcity to understanding meaning requires extraordinarily specific ones.
What is the difference between "English Speaking People" and "the Chinese Room" ? The problem with Searle's arguments is that all the Chinese room is is an appeal to absurdity, a sleight of hand. I'm supposed to think, "Oh. This is so absurd, of course the room doesn't understand" but it is an appeal that falls apart about once you realize that the same logic could be applied to any computational process, including human cognition. The distinction Searle draws between a person who genuinely understands English and a system that mechanically manipulates symbols is, in essence, arbitrary. They are both systems that have demonstrated understanding.