Coefficient comparison conjecture for logarithmic and ordinary étale motives

Let $k$ be a field, and suppose that $\Lambda=\mathbb{Z}/n$, where $n$ is invertible in $k$. Let $\operatorname{DM}^{\mathrm{eff}}_{\log,\acute{e}t}$, $\operatorname{DM}^{\mathrm{eff}}_{\log,\acute{e}t,\mathrm{prop}}$, $\operatorname{DM}^{\mathrm{eff}}_{\log,l\acute{e}t}$, $\operatorname{DM}^{\mathrm{eff}}_{\log,l\acute{e}t,\mathrm{prop}}$, and $\operatorname{DM}^{\mathrm{eff}}_{\acute{e}t}$ denote the corresponding effective motive categories, with the superscript $\mathrm{prop}$ indicating the proper variant.

Coefficient comparison conjecture. There are equivalences of triangulated categories

$$\operatorname{DM}^{\mathrm{eff}}_{\log,\acute{e}t}\leftarrow \operatorname{DM}^{\mathrm{eff}}_{\log,\acute{e}t,\mathrm{prop}}\rightarrow \operatorname{DM}^{\mathrm{eff}}_{\acute{e}t},$$

and

$$\operatorname{DM}^{\mathrm{eff}}_{\log,l\acute{e}t}\leftarrow \operatorname{DM}^{\mathrm{eff}}_{\log,l\acute{e}t,\mathrm{prop}}\rightarrow \operatorname{DM}^{\mathrm{eff}}_{\acute{e}t}.$$

This predicts that both logarithmic étale theories compare with ordinary étale motives through their proper variants. The source presents it as an expectation and gives partial evidence, but no proof or disproof.