So this is something of a general Sanskrit question and less of a question to do with specifically Buddhist texts.
So adhyātma, afaik, means “inside yourself” as far as its purposes in Buddhist Hybrid Sanskrit are.
In Hinduism, it refers to some kind of oversoul. There is such a thing as the Aḍhyāṭma Upaniṣad, where the usage of aḍhyāṭma seems to be more-or-less the same as the Hindu usage of adhyātma.
Where does aḍhyāṭma come from? Why these diacritics? I’ve never seen adhi- written with a ḍ or -ātma written with a ṭ. Are they different words?
The basic meaning of adhyātma is “pertaining to oneself”. In a recent thread we saw an example of that in ajjhattasanti, “inner peace”. I haven’t studied the Hindu usage, but it’s quite possible that a metaphysical sense like “oversoul” developed over time.
Bahirdha just means “external, outside oneself”. “External minds” means “the minds of other people”. When combined with adhyatma, the sense is of synthesis; seeing that these things are really the same.