What is a subjective experience? To me, this seems like an infinite regress problem.

Subjective experience is the awareness of an internal representation.

What is awareness then? Do you see my point? Either you end up with a circle of references or an infinite regress of definitions to describe the ineffable.

It’s the problem of qualia [1]. They can’t really be defined, only pointed at. My experience of seeing the colour red is non-universalizable. Thus the word red can only point at it, it can’t describe or define it.

[1] https://en.wikipedia.org/wiki/Qualia

I would say there is no working definition of consciousness at all—and potentially there can’t be a complete and provably correct one, if we assume Gödel’s incompleteness theorem is true. The reason is that our arguments about consciousness originate from consciousness itself, we are building a model of the system while being inside of it. The only definitive statement that can be made, I guess, is that consciousness exists.

As far as consciousness that doesn’t react, there are materialist/behaviourist/illusionist views that hold that only observed behaviour matters and anything else may well not exist, but I personally am not convinced by them.