To quote Wikipedia:
"While other knowledge could be a figment of imagination, deception, or mistake, Descartes asserted that the very act of doubting one's own existence served—at minimum—as proof of the reality of one's own mind; there must be a thinking entity—in this case the self—for there to be a thought."
Similarly, the claim that if s thinks then s exists does not entail that a further claim that thinking is central to s's personhood.
That is not Descartes conclusion or my conclusion.
To Descartes, the person as experienced in a priori thought has a special primacy over all other existing things. While "s" may be doubted due to its a posteriori nature, the self is fundamentally undoubtable in its existence, hence "I think therefore I am".
To Descartes, the existence of a priori thought is the building block of all logic and personhood.