I am not sure what you mean by the scientific method. The scientific method can be as simple as trial-and-error or observation, such as the idea that maybe you shouldn't eat a certain berry if you just watched someone eat one right before they passed out and started foaming at the mouth. Animals without highly developed language do this all the time.
There is no doubt that writing out or sounding out your reasoning can boost your ability to think and communicate. For example, it can promote a dialectic which can refine your ideas, and you can even have an inner dialogue using language. It can also help you form a representation of the thought process for communication.
But it can also muddle your thinking or leave you with blind spots if the language is not expressive enough or you rely on it too much. You do not need a linguistic representation of a concept in order to reason about it (well, I don't seem to and I doubt I'm special in that regard).
Just because an internally consistent language may be sufficient for basic reasoning doesn't mean it's necessary overall, or that it doesn't place a 'ceiling' on the types of thoughts you can think. I would argue that it cuts both ways.
It is definitely interesting that you seemingly get reasoning "for free" when you only optimize for language (e.g. large language models). But that is the way it would be if grammar was a more formal descendant of logic.
Maybe this is why authentic geniuses, or people capable of coming up with ideas not commonly in circulation, often have a hard time explaining their ideas (see https://kottke.org/13/05/the-three-types-of-specialist)