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In this paper we study Cuntz--Pimsner algebras associated to$\mathrm{C}^*$-correspondences over commutative $\mathrm{C}^*$-algebras fromthe point of view of the $\mathrm{C}^*$-algebra classification programme. Weshow that when the correspondence comes from an aperiodic homeomorphism of afinite-dimensional infinite compact metric space $X$ twisted by a vectorbundle, the resulting Cuntz--Pimsner algebras have finite nuclear dimension.When the homeomorphism is minimal, this entails classification of these$\mathrm{C}^*$-algebras by the Elliott invariant. This establishes a dichotomy:when the vector bundle has rank one, the Cuntz--Pimsner algebra has stable rankone. Otherwise, it is purely infinite.  For a Cuntz--Pimsner algebra of a minimal homeomorphism of an infinitecompact metric space $X$ twisted by a line bundle over $X$, we introduceorbit-breaking subalgebras. With no assumptions on the dimension of $X$, weshow that they are centrally large subalgebras and hence simple and stablyfinite. When the dimension of $X$ is finite, they are furthermore$\mathcal{Z}$-stable and hence classified by the Elliott invariant.

$\mathrm{C}^*$-algebras associated to homeomorphisms twisted by vector bundles over finite dimensional spaces