The slowest-growth conjecture outside the order-interpretable class

Let $c9$-categorical mean categorical in every infinite cardinality, and for an $c9$-categorical structure $c4$ let $u_n(c4)$ be the number of orbits of $c0 goperatorname{Aut}(c4)$ on $n$-element subsets of $c4$. Let $a4$ be the countable circular order and let $b2c4a0$ denote its betweenness relation.

Slowest-growth conjecture. If an $c9$-categorical structure $c4$ is not interpretable in $(\mathbb Q;<)$, then

$$u_n(c4)\geq u_n((\mathbb S;\operatorname{Betw}))$$

for all sufficiently large $n$.

The claim formalizes the observation that the circular-order betweenness structure appears to have the slowest known unlabelled growth outside the class of structures interpretable in $(\mathbb Q;<)$. It remains open.