Quantum-liquid TQFTs as complete invariants of bordisms

Let $f$ and $g$ be $n$-morphisms in the oriented bordism category $\mathbf{Bord}^{\mathrm{or}}_n$. Completeness conjecture. If $f$ and $g$ are not equivalent, then there exists a symmetric monoidal functor

$$Z:\mathbf{Bord}^{\mathrm{or}}_n\to\mathcal{QL}_{\mathrm{sk}}^n$$

such that $Z(f)$ and $Z(g)$ are not isometric in $\mathcal{QL}_{\mathrm{sk}}^n$. This asserts that oriented extended TQFTs arising from quantum liquids separate nonequivalent bordisms and therefore provide a complete invariant for the topological information of compact smooth $n$-manifolds; the source gives no resolution.