Quadratic saturation conjecture for the convex geometric matching $M_3$

Let $M_3$ be the convex geometric matching denoted by $M_3$ in the source, and let $\operatorname{sat}_\circlearrowright(n,M_3)$ denote its saturation number on $n$ vertices. Quadratic saturation conjecture for $M_3$.

$$\operatorname{sat}_\circlearrowright(n,M_3)\sim \frac{3}{2}n^2.$$

The paper has an upper bound for the saturation number of $M_3$ and states that this upper bound is suspected to be asymptotically tight; the equivalent remains open.