Coherent EPPA for finite two-graphs

Determine whether the class of all finite two-graphs has coherent EPPA.

Background

Finite two-graphs have EPPA, but the known witnesses are not coherent. They are therefore a concrete candidate for a class with EPPA but without coherent EPPA.

References

Does the class of all finite two-graphs 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