The right-triangle stability conjecture for the constant $C_{\rm st,2}$

Let $T$ be a triangle with maximal interior angle $\omega$, and let $C_{\rm st,2}$ denote the stability constant associated with the hybrid high-order method. For any $p\in\mathbb N_0$, stability conjecture. If

$$\omega\leq\pi/2,$$

then

$$C_{\rm st,2}\leq\sqrt{2}.$$

This conjecture is based on numerical evidence for triangles with maximal interior angle at most $\pi/2$; the supplied text does not indicate whether it has been proved or disproved.