I have OrthancExplorer2.UiOptions.DateFormat set in orthanc.json to MM/dd/yyyy.
This seems to affect only one thing - the Study Date search box. It does not affect the “Display format for dates in the study list” (which remains dd/MM/yyyy), even though that is what the comments for that option say it does in orthanc-explorer-2/Plugin/DefaultConfiguration.json at master · orthanc-server/orthanc-explorer-2 · GitHub
Finally, it does not affect the format for entering dates when editing DICOM tags (though this is probably to be expected given the date field there is not implemented as date input; it would be nice if it were.)