When Using AI they say "Context is King". "Reasoning" models are using the AI to generate context. They are not reasoning in the sense of logic, or philosophy. Mirage, whatever you want to call it, it is rather unlike what people mean when they use the term reasoning. Calling it reasoning is up there with calling generating out put people don't like hallucinations.
You are making the same mistake OP is calling out. As far as I can tell “generating context” is exactly what human reasoning is too. Consider the phrase “let’s reason this out” where you then explore all options in detail, before pronouncing your judgement. Feels exactly like what the AI reasoner is doing.
Put another way, LLMs are good at talking like they are thinking. That can get you pretty far, but it is not reasoning.