I don't think "mental" has to be so seperated from the biological components. You could think about it more like cognition and thought are processes in which the brain taps the neurons to make decisions.
Like a computer that relies on its code to generate output, the brain relies on experiences / memories (which is also knowledge) to come to a conclusion on things. When we see artificial intelligence "make decisions", it gathers information and instructions programmed into it, and carries out procedures, like jumping out of harm's way for example. Yet we don't question if the computer is "thinking" or not, and if there's some kind of entity that carries these thoughts out. I think we view "thought" and "cognition" as some kind of magical phenomena because we can't fully explain the complexity of it yet, nor are we even close.
my two cents at least.