How can you express the average treatment effect on the treated (ATT) in Pearl's do notation? How can you express the average treatment effect on the treated (ATT) in Pearl's do notation?
Would it be $E(Y|X=1,do(X)=1)-E(Y|X=1,do(X)=0)$?

You cannot express it in "do" notation! The conditioning event $X = 1$ would conflict with $do(X = 0)$.
Indeed, the ATT is an example of a counterfactual/"rung 3" causal query that is strictly "deeper" than just an interventional "do"-query. See
Pearl, Judea. "The seven tools of causal inference, with reflections on machine learning." Communications of the ACM 62.3 (2019): 54-60.
