The thinking entity that is proven to exist is the person. To descartes that thinking entity is the very core and fundamental unit of the person. The body and the interactions with others is irrelevant to that core.
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.