Motivated Grothendieck period conjecture in terms of periods and motivated Galois groups

Let $M\in\mathcal{M}_{\overline{\mathbb{Q}}}^{\mathrm{And}}$ be an André motive. Let $G_{\mathrm{And}}(M)=\operatorname{Aut}^{\otimes}(H_B|_{\langle M\rangle})$ be its motivated Galois group, let $P(M)$ denote its periods, and let $\overline{\mathbb{Q}}(P(M))$ be the subfield of $\mathbb{C}$ generated by these periods over $\overline{\mathbb{Q}}$. Let $\Omega^{\mathrm{And}}_M$ be the motivated torsor of periods.

Motivated Grothendieck period conjecture. The motive $M$ satisfies MGPC if $\Omega^{\mathrm{And}}_M$ is connected and

$$\operatorname{tr.deg}_{\mathbb{Q}}\overline{\mathbb{Q}}(P(M))=\dim G_{\mathrm{And}}(M).$$

This is an equivalent reformulation of the MGPC in terms of the connectedness of the period torsor and the transcendence degree of the field generated by periods. The source gives no evidence that the conjecture has been resolved.