Our new paper Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing (with Marek Černý) has been accepted at STACS 2026. In this paper, we tightly characterise the complexity of deciding homomorphism indistinguishability over CSMO2-definable graph classes of bounded treewidth and bounded pathwidth. In the bounded-treewidth case, this problem reduces to polynomial identity testing (PIT) and can be PIT-complete. In the bounded-pathwidth case, this problem is in C=L and can be C=L-complete.