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To use $S$ as the apparatus, prepare it in the ready state $|+{⟩}_S$ and later read it in the Hadamard basis. For an arbitrary input $\alpha |+{⟩}_D+\beta |-{⟩}_D$, part (b) givesThe two apparatus states are orthogonal, so its readout measures the corresponding projectors on $D$ and preserves each input eigenstate. The observable iswith outcomes $+1$ and $-1$. This is the measurement direction of a CNOT interaction in the complementary basis.

The ready state and readout basis matter. Keeping $S$ in the original $|0{⟩}_S$ would make the old-basis controlled gate act as the identity on $D$, producing no record. Thus the same interaction can serve either measurement direction, with different apparatus preparation and pointer readout; the Hamiltonian operator alone does not assign an intrinsic system/apparatus role.