The AR are the Authority Requirements, so its only logical the competencies for Authority Inspectors to affect mostly the part AR than the part OR (Organisational Requirements).

I disagree.

I believe the spirit of the ED is to have NAA Inspectors trained on auditing the implementation of Part-IS witin organisations, not to audit the internal implementation within NAAs.

That will most probably be the first requirement, as Part-IS.D.OR becomes applicable before Part-IS.AR.

For example, point number 3 reads:
"Evaluate how an organisation has identified and documented the aviation safety relevant assets that are in the ISMS scope."
It specifically talks about an organisation implementation, and yet it is mapped to IS.AR.205(a)(b)

IS.AR.205(a) reads "The competent authority shall identify all the elements of its own organisation [...]"
So it has nothing to do with "Evaluate how an organisation has [...]".

This is a common misconception I encounter when talking to NAAs, so I am not surprised to see it. However, I think it should be corrected for the sake of clarity.

Or at least, there should be no reference to AR/OR when the requirements are identical in AR and OR.
Or there should be two mappings, one for NAA inspectors auditing Organisations (under D.OR or I.OR) and one for NAA inspectors auditing Authorities (under AR).