Awkwardly synthesizing jobermark's old question Is there a boundary on 'physical'? with my (badly put) question Can physics talk about non-physical entities/concepts, and if not which academic department does?, finally pinpointing (I hope) what bugs me.
Let me start with what I'm hoping to find:
Non-physical having causal effects on the physical (and vice versa).
Clear enough definition (no matter how general it is) of physicality that'll distinct between physical and non-physical, or, will provide boundaries of physicality.
A definition of physicality that'll account for the history of physics, the changes on how we viewed physics and non-physics.
Not a dualistic solution.
In jobermark's question he presents the idea that the definition of physicality is so vague that it always expands and encompass what was in the past not considered physical (similar, in general, to the vagueness of "the scientific method"). Then he goes to state that this makes the distinction between physical and non-physical as near non-existent nowadays*.
My question was about the academic scope of this question, as in, not only conceptually, but practically - is a physicist able to talk about the non-physicality. This question seems more clear to me after going through jobermark's because it means that the physicist, if he talks about non-physical entities, might not know that it's in fact what he does because to him it seems like physical entities (because of, again, the vagueness of the definitions).
So after pinpointing that the root of the issue was at the definition level (which I basically tried to ignore in my question), and where jobermark's answers weren't suffice (at the end I think he took a turn in his answer, which seems to me like a bit of avoiding the problem) because while admitting the problem they haven't really provided a concrete answer (maybe there isn't one, and if so this question can be deleted).
So, my question will be - is there any clear enough definition of physics that answer the 4 requirements I've stated above?
(*although there are the ways that's been shown in the answers to Alexander's question How can something non-physical exist?, the first positing the distinction in abstractness/concreteness but agrees to providing physicality all of the causal realm [which isn't what I'm seeking]; the second doesn't really distinct them but rather takes a sort of holistic/monistic approach, which isn't bad but doesn't yet answers the question to its full extent [even in this holistic approach one needs to distinct where the physical end and the non-physical starts]; and another answer distributes the physical and non-physical to different areas of existence, which [I think] renders every attempt to bring non-physical causality to science as futile)