It's as if a LLM is only one part of a brain, not the whole thing.

So of course it doesn't do everything a human does, but it still can do some aspects of mental processes.

Whether "thinking" means "everything a human brain does" or whether "thinking" means a specific cognitive process that we humans do, is a matter of definition.

I'd argue that defining "thinking" independently of "volition" is a useful definition because it allows us to break down things in parts and understand them