The notion of a conscious model of oneself as an individual entity actively trying to establish epistemic relations to the world and to oneself, I think, comes very close to what we traditionally mean by notions like "subjectivity".

When you are simply observing your breath, you are perceiving an automatically unfolding process in your body. By contrast, when you are observing your wandering mind, you are also experiencing the spontaneous activity of a process in your body.

Only as long as we believe in our own identity over time does it make sense for us to make future plans, avoid risks, and treat our fellow human beings fairly - for the consequences of our actions will, in the end, always concern ourselves.

You cannot be a rational subject without veto-control on the level of mental action.

I believe that if we would carefully apply the distinction between transparency and opacity to the different layers of the human self-model, looking at self-consciousness in a much more careful and fine-grained manner, then we might also arrive at a new answer to your original question: What a "first-person perspective" really is.

I believe we should really take our own phenomenology more seriously. What a good theory of conscious must explain is the variance in this subjective sense of realness: There clearly is a phenomenology of "hyperrealness", for example during religious experiences or under the influence of certain psychoactive substances.

A lot of evidence shows that most of our cognitive processing is unconscious - phenomenal experience is just a very small slice or partition of a much larger space in which mental processing takes place.