As i understand it.
Behaviorism which ignores the underlying philosophical framework of behavior altogether whilst focusing on reward circuitry & conditioning of pattern recognition, shows that to an extent behavior is dictated by classical conditioning.
This is how one would train a dog with reward/punishment and more or less ignoring what he thinks.
Neuroscience developed in course of the development of psychopharmacological research and was predicated on hardcore behaviorism & molecular biology.
Eventually it became evident that the subjective philosophy of a person impacts his values & behavior as well but there was little to no study of this.
At this point consciousness research and cognitive behavioral therapy were in the infancy and pople wanted to study the psychological effects of character-changing experiences such as spiritual, mystical or great learning.
The natural course is that this would be still an extention of pharmacology and therefore the academic consciousness study turned to researching psychedelic drugs.
I think it can be summed up that behavioral science holds a person's understanding of the context of his experiences shapes his motivations and circumstances shape the behavior circuitry accordingly.
Afaik as to Anatta in particular, scientific litterature makes a strong case for there being no free-will, rather there being conditioning only and that neurobroadcasting is a reliable predictor of behavior and that maybe more so than a person's own philosophy which is generally more or less speculative & with cognitive dissonance.
Another interesting point is that there is some litterature on what exact brain activity is associated with the notion of self and the way this plays out has been surprising to people as it's not what a naive person would expect.
Eg when people think about death, what lights up are regions that are associated with other beings rather than that which has to do with oneself.
Here a person would say that he/she or that "self" thinks that death is something that applies to all beings but the circuitry tells a different story and the circuitry is the actual behavioral wiring.
If there indeed was an element of self then one would expect a different circuitry.
The field of 'general semantics' is probably closest to understanding anatta.
General semantics is concerned with how electrocolloidal events are abstracted as objects of perceptions, how these are further classified by words for thought, how these words are likewise more or less of an abstraction and how we might gain a measure of control over our own behavior & mental wellness through insight.
Imo one could say that general semantics establishes the emptiness of words and explains how delusion about these truths is a mental illness.