Depends what you define as a metaphysical entity. Some would say that the number four is a metaphysical entity. You cannot find the number four anywhere in the physical world. You can have objects that possess the quality of "fourness" in the physical world (like four apples in a bowl), but not the pure concept of four.
Similarly, the notion of a perfect circle can be considered a metaphysical entity: you can have imperfect examples of circles in the physical world, but the concept of a perfect circle is itself metaphysical, as no perfect circles exist in the physical world.
Equally, you could consider any software (both in a computer, or in the brain — and by the latter I mean things we learn and store as data structures in the brain) as metaphysical.
These idea date back to Plato, and his theory of forms. Plato posited that there were three worlds: the physical world, the world of forms, and the chora (the world prior to all forms). Plato said that perfect circles could only exist in the world of forms, but never in the physical world. Only imperfect examples of circles can exist in the physical world. Plato said that the fact we can mentally conceive of a perfect circle indicates that our minds have access to the world of forms.
Thus Plato believed our mind has access to both the physical world (via our senses), and to the world of perfect forms. Plato's theory is taken very seriously, even today.
As far as the problems with psychiatry are concerned, I think the computer hardware/software analogy is useful to express the issues here. We can take the physical brain to be the hardware, and the learned information and learned responses we have acquired in life to be the software that runs on our physical brain. So the knowledge of how to ride a bike would be an example of brain software that we have learned, which exists as data stored in our brain.
I think what you are getting at (and I agree with you), is that psychiatry has historically often assumed that the causes of mental and/or cognitive diseases (diseases like ME/CFS, anxiety disorders, clinical depression, anorexia, bipolar, autism, schizophrenia, etc) are to be found in the software of the brain, and therefore, psychiatry has used what it considerers to be corrective measures (like psychotherapy) to fix what it assumes is broken brain software.
But throughout the whole of the 20th century, when psychiatry championed this software approach to mental and/or cognitive ill health, psychiatry never really got to the bottom of these diseases, and never discovered their causes. At best, they achieved some minor improvements in the symptoms.
So what psychiatry needs to do in the 21st century is now focus on the hardware side, focus on the physical brain, and study how dysfunctions in the physical brain cause mental and/or cognitive ill health. The physical side of the equation has for too long been neglected.
I think this is what you are getting at, A.B., and I am in agreement.
I have to say, though, that although I used to love these subjects and their hair-splitting concepts, these days, with ME/CFS, I unfortunately don't really have mental clarity to get into them anymore. (Or should that be: "I don't have the brain clarity"?)