Have you read those papers?
The first paper says in the intro:
The aim of this paper is to raise questions for discussion and debate
on academic identity rather than to offer definitive answers or
specific conclusions. In particular, the paper addresses the following
1. What is academic identity?
2. What is it to be an academic in modern times?
3. What are the pressures that academics work under?
Then, at the beginning of the section on what is academic identity:
Academic identity is a phrase that is discussed in the Higher
Education sector as if it is a fixed and known thing. Academic
identity lacks precision in terms of description and cannot therefore
be summed up in a few sentences.
This indicates that there is no (at least agreed-upon) definition. I didn't read the paper, but it seems that this section indicates what are the key commonalities in various situations of "academic identity." (I've never heard the term myself.)