Spectrality conjecture for the Kolmogorov quotient of infinite affine orbit space

Let $K$ be a field, let $n$ be a positive integer, and let $G$ act on the infinite affine space ${\mathbb A}^n_{K,\infty}$. Write $\textnormal{KQ}({\mathbb A}^n_{K,\infty}/G)$ for the Kolmogorov quotient of the orbit space, obtained by identifying topologically indistinguishable points. Spectrality conjecture. The Kolmogorov quotient

$$\textnormal{KQ}({\mathbb A}^n_{K,\infty}/G)$$

is a spectral space. The quotient removes the failure of the $T_0$ condition in the orbit space. Cohen's classical result shows that this space is noetherian; the conjecture asserts the stronger spectral-space property.