My self is whatever is making decisions. If some scientist somewhere chops words and slices definitions and does some measurements and declares that my "self" isn't what is "making decisions", then they've been misled by bad philosophy into making stupid statements. And I use the word "stupid" carefully.
I am completely unfazed by the fact that what I intuitively thought the process might have been isn't the real process. The entire history of science from start to finish has been the unrelenting story of taking a closer look at something than we ever have before, and being surprised by what we found. The exceptions to that, such as predicting antimatter or the Higg's boson, are notable stories precisely because they are exceptions. Nevertheless, those surprises never negate our previous experiences. They reveal unexpected sources and surprising nuances, but the fact that we were surprised by where our higher-level concepts came from reveal that our previous understanding was in error, not the higher level concepts. Water has been wet for the whole of human experience, no matter whether it was its own element, or a essence, or a composition of atoms, or a pattern of fluctuations in quantum fields, or whatever the final Grand Unified Theory might declare it "really" is. Our understanding of water has been greatly enhanced by those advances, but it remains wet.
Nevertheless, my self is whatever is making decisions. The only way to break me off that definition would be to remove the entire "making decisions" part, which gets into its own philosophical thicket. Even in a fully deterministic universe I may still be "making decisions", despite popular belief to the contrary; one must simply be more careful about the definition of "making decisions" but meaningful definitions can still be produced.
There's a very long history of this sort of word chopping. Declaring this or that thing an "illusion" simply because it isn't exactly what we thought it was, or because it turns out not to be an atomic object of its own in the universe (hardly surprising since the only atomic things that seem to actually exist in this universe aren't very philosophically exciting, like quarks and electrons) is one very common tell, but it's not the only one. Consciousness gets a lot of stories like this where someone tries to manipulate words to "reveal" conscious experience is some sort of fake or something, but amazingly, not a single one of them has affected my own personal conscious experience. Per Descartes, as the existence of my own conscious experience is arguably the single thing I have the most confidence about, arguably the only thing I am 100% certain of, I find myself rather unimpressed with attempts to deny it. The fact that a certain subset of scientists are perturbed by their inability to wrap numbers around it is their problem, not mine. They are welcome to try to explain it; any attempts they make to explain it away can be discarded without further examination.