EPPA for finite tournaments

Determine whether the class of all finite tournaments has EPPA and, if so, whether it has coherent EPPA.

Background

The problem is equivalent to a question in profinite group theory. Standard EPPA constructions produce unspecified pairs whose orientations must later be chosen, and completing them to tournaments may destroy automorphisms.

References

Does the class of all finite tournaments 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