You can just look at the definitions and see whether they apply.

The relevant MW definition for "reasoning" is: "the use of reason, especially: the drawing of inferences or conclusions through the use of reason."

And "reason" is: "the power of comprehending, inferring, or thinking especially in orderly rational ways."

Functionally speaking, i.e. in terms of observable behavior, LLMs exhibit comprehension, inferring, and reasoning. If someone wants to object to that, they'd need to explain what relevant property prevents a conclusion drawn by an LLM from being counted as involving reasoning.