Morel's rational motivic cohomology identification conjecture

Let $S$ be a derived scheme. Write $\mathrm{H}\mathbb Q$ for the rational motivic cohomology spectrum over $S$, and let $\mathbb{1}_{\mathbb Q}^+$ denote the positive eigenspace in the decomposition

$$\mathbb{1}_{\mathbb Q}=\mathbb{1}_{\mathbb Q}^+\times\mathbb{1}_{\mathbb Q}^-$$

of the rational motivic sphere induced by the swap automorphism of $\mathbb P^1\otimes\mathbb P^1$. Morel's conjecture. For any derived scheme $S$, there is an equivalence

$$\mathrm{H}\mathbb Q\simeq \mathbb{1}_{\mathbb Q}^+$$

in $\mathrm{MS}_S$. This extends the known identification in the regular noetherian setting and asks whether it remains valid in the larger category of motivic spectra over arbitrary derived schemes.