Conjecture on the clique number in the intermediate regime

Let $G_{n,r_n}$ be the split-and-drift random graph, let $_n$ denote its parameter, and let $\kappa_n$ be its clique number. In the intermediate regime, $r_n \to +\infty$ and $r_n=o(n)$. Clique-number conjecture. There exist constants $\alpha,\beta>0$ such that

$$\mathbb{P}\left(\alpha\frac{n}{r_n}\leq \kappa_n\leq\beta\frac{n}{r_n}\right)\xrightarrow[n\to\infty]{\mathstrut}1.$$

The conjecture predicts that the clique number is of order $n/r_n$, matching the approximate degree scale of a typical vertex in the intermediate regime. The source provides no resolution, so the conjecture remains open.