Let $X$ be a scheme and denote by $Et(X)$ the associated étale homotopy type. Then by the work of Artin-Mazur, we know that for an abelian group $A$, we have $$H^n(Et(X),A)=H^n_{ét}(X,A)$$ and
$$\pi^1(Et(X))\cong \pi^1_{alg}(X).$$ Therefore I wonder what $H_n(Et(X),A)$ is? Naively I would hope that it is $H_{n,ét}(X,A)$, however, no survey or reference mentions this.

$\DeclareMathOperator\Et{Et}$Let $X$ be a scheme and denote by $\Et(X)$ the associated étale homotopy type. Then by the work of Artin–Mazur, we know that for an abelian group $A$, we have $$H^n(\Et(X),A)=H^n_{\text{ét}}(X,A)$$ and
$$\pi^1(\Et(X))\cong \pi^1_{\text{alg}}(X).$$ Therefore I wonder what $H_n(\Et(X),A)$ is? Naïvely I would hope that it is $H_{n,\text{ét}}(X,A)$, however, it seems that no survey or reference mentions this.