Cowling's conjecture for Hausdorff étale groupoids

Let $\mathcal{G}$ be a Hausdorff étale groupoid. Weak amenability means that $\Lambda_{\text{cb}}(\mathcal{G})$ is finite, and the condition $\Lambda_{\text{cb}}(\mathcal{G})=1$ is the groupoid analogue of Cowling's hypothesis. Cowling's conjecture. If $\mathcal{G}$ is weakly amenable with $\Lambda_{\text{cb}}(\mathcal{G})=1$, then it has the Haagerup property. The conjecture asks whether the group-theoretic implication extends to Hausdorff étale groupoids; the source presents it as an open question and gives no resolution.