I haven’t read the books of Edward T. Hall. I’ll add him to my reading list!
I’m sort of new to the language/culture discussion, but based on what I’ve read, it seems as though we think using language. So, if English has evolved to reflect a certain English way of thinking, your thinking will be influenced by that if you think in English. If, on the other hand, you think in Japanese, your thinking will be influenced by using that language.
That doesn’t mean all English people think one way and all Japanese people think another way. But the English and Japanese languages will pick up and reinforce certain common ways of thinking from the people using them. For example, if people in my culture have a nuanced way of thinking about greed, our language will evolve until we have the vocabulary to express that nuance. Then, if you’re thinking about greed in that language, your thinking will likely be nuanced as well.