Why I mention this is that I see both language and reasoning as rooted in this more fundamental cognitive ability of "coherent sequencing". This sits behind all kinds of planning and puzzling tasks where you have to project forward a sequence of theoretical actions and abstractly evaluate the outcome.
Which is all to say, I don't think language and reasoning are the same, but I do think it is likely they stem from the same underlying fundamental mechanisms in our brain. And as a consequence, it's actually quite plausible that LLMs can reconstruct mechanisms of reasoning from language, in a regressive model kind of fashion. ie: just because their are other ways to reason doesn't exclude language as a path to it.