Here's my take on it:
Enlightenment is a state of relative understanding. It simply means you have become clearer on the nature of being than you were previous to some insight. There are endless steps in enlightenment. Every step up in clarity is enlightenment relative to your previous understanding. Some steps are more significant than others, such as: when one awakens to the realization that one is not what one thinks one is. And that what one truly is is the awareness, the spacious presence, within which all experience, including thinking, takes place.
So why should "I" bother becoming enlighted?
Only because in the effort, clarity of being increases. But as an end game, probably not worth the effort as there is no end to arrive at. There's only ever greater understanding and clarity.
Then I get this question, this "I" that brings the attention back to the Awareness cannot be me, because I'm aware of that too.
This is a bit of a misdirect. The reality is that 'awareness' and 'I' are symbiotic in nature. I-dentity is a unique perspective that exists within awareness. There are infinite unique perspectives. You and I and everyone in the world are unique perspectives within awareness. If it were just awareness why are you not aware of everything that exists? It's because of the relationship between the 'I' that is the perspective that is you, and the uniqueness it offers within awareness. The primary distinction between what one 'individual' experiences and 'another' is the uniqueness of their perspective.
this "I" that brings the attention back to the Awareness cannot be me, because I'm aware of that too.
There is the appearance that you are aware of the I, but look a little closer. You are aware of the 'I' as it shifts around within awareness because of its natural fluidity to focus attention. Whatever the I chooses to focus on, awareness is always there. In the precise moment of conscious experience however, 'I' and awareness are one and the same. What appears to be an awareness of 'I' is actually the experience the 'I' had in retrospect, and the experience includes the 'I' perspective itself as it was in the moment. But that's history. What appears to be an awareness of the 'I' is just a remembrance of the 'I' as it was a moment ago.
Everything the 'I' focuses on is within the awareness that is uniquely you by virtue of perspective. And the moment the 'I' creates a focus and experience, it becomes historical and a matter of memory awareness. So yes, you are aware of the 'I' that does this or that, or thinks this or that, because it is a matter of historical experience rather than the 'I's' true nature of present beingness. It is but a memory of what 'I' was, even if only a nano second later.
The true 'I' is you as a unique, individualized perspective of awareness. All recognition of 'I' is done so in a historical context. One can only point to the 'I' in historical context. However, one can only experience their beingness, their true self, who they are, in the present moment, and that is the 'I' as unique perspective living awareness.