EPPA for reducts of uniform hypergraphs

Classify which reducts of the k-uniform random hypergraph, for k≥3, have EPPA and coherent EPPA.

Background

Thomas's classification shows that these reducts correspond to switching operations, but EPPA is unresolved for all nontrivial cases and the known two-graph construction does not appear to generalize.

References

Which reducts of the $k$-uniform hypergraph, $k\geq 3$, have (coherent) EPPA?

— Twenty years of Nešetřil's classification programme of Ramsey classes  (2501.17293 - Hubička et al., 28 Jan 2025) in Question, subsection EPPA