= Solution
Among observed pretreatment variables, every sufficient set must contain $M_1$ to block
$$
Z_1\leftarrow M_1\to C\to Y
$$
and $Z_3$ to block
$$
Z_1\leftarrow S\to Z_3\to Y.
$$
Conditioning on $Z_3$ opens the <collider> on
$$
Z_1\leftarrow S\to Z_3\leftarrow M_3\to C\to Y,
$$
so $M_3$ must also be included. The resulting minimal <sufficient adjustment set> is
$$
X_0=\{M_1,M_3,Z_3\}.
$$
It blocks every path from $Z_1$ to $Y$ that remains after removing $A\to Y$, while the open path
$$
Z_1\leftarrow S\to Z_2\to A
$$
preserves <instrument relevance>. Adding $M_2$ blocks no required relevance path, so
$$
X_1=\{M_1,M_2,M_3,Z_3\}
$$
is also sufficient.
There are no others. In particular, adding $Z_2$ blocks the displayed relevance path. Without $M_2$, conditioning on $Z_2$ also opens
$$
Z_1\leftarrow S\to Z_2\leftarrow M_2\to C\to Y,
$$
which violates independence; adding $M_2$ closes that path but leaves no open path from $Z_1$ to $A$. Hence the complete list is $X_0$ and $X_1$.
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