Psychology is the study of 'the mind', and however poorly defined that may be even within the field itself, it is depicted as more of a spiritual entity than a biological one

Absolute tosh. Psychology is modelling the functioning of the brain in an abstract, top-down way while neuroscience is modelling the brain in a concrete, bottom-up way. They are both, however, "merely" seeking to provide conceptual models explaining the behaviour of biological processes in the brain.

Psychology is necessarily a softer science than neuroscience, but neither one has anything to do with supernatural nonsense like spirituality or "souls".

Moreover, regardless of whether psychology is top-down or bottom-up, it's still an attempt to explain the functioning of the brain, which is most definitely applied biology.

It's like a software/hardware difference. Software deals in rarefied, abstract models that don't necessarily have any direct correspondence to the underlying mechanisms of the hardware substrate they run on, but ultimately, at its core, functionally software is "just" applied hardware.

Ultimately when you instantiate a new object using a class that implements an AbstractThingyFactoryFactory interface in Java, what you're actually doing is specifying that specific patterns of electrons should flow through specific wires and circuits in the motherboard, RAM and processor. You're saved from caring about which exact patterns they are and which exact processor it is (one of the great benefits of using a higher-level language over something like assembly), but functionally all your fancy code still merely boils down to "send electrons down this wire" and "open or close these particular transistors".

Sure you don't normally think about it like that, but (at a very high, abstract level) that's still exactly what you're doing.