> I notice the recent turkey / Syria quakes occurred on the day of the full moon. Since tidal stresses peak at new and full moons, this seems like an interesting coincidence. Is there any correlation with quake timing and moon phase.

While slightly under the cutoff for the particular analysis in this paper, Hough, 2018 succinctly sums up the extent to which lunar phase has anything to do with earthquakes. As discussed in this paper (with citations to relevant papers), there are a variety of suggestions that there may be real correlations between lunar phase and some details of earthquake statistics in certain magnitude ranges or settings. Importantly though, and especially in the context forecasting, these tend to be global correlations, e.g., for certain earthquakes and certain systems, there might be a slightly higher probability of earthquakes occurring in relation to tidal stresses, but this tells you nothing about specific risk on any specific fault or location so it has pretty minimal utility for actual, meaningful prediction or even contribution to forecasting.

> I’ve previously also seen a study indicating more larger earthquakes occur during a certain phase of a 30 year cycle of earth’s interday rotation time variation. The prediction was more earthquakes would occur in the 5 years following the peak of the variation cycle. The peak was in 2017. Has there been any validation of an increase in large magnitude quakes during the past 5 years?

Without any real detail to go on there, I'm going to guess you're thinking of this paper by Bendick & Bilham, 2017 which was published in 2017, not suggesting a peak in 2017? There has been a follow up in the sense of later papers like Bendick & Mencin, 2020 finding additional support for "synchronization" in global earthquake catalogs. The crucial bit (and this is also discussed in Hough, 2018 more directly) is that generally papers like this are fundamentally misinterpreted by the media and lay audience. Both the Bendick & Bilham and later Bendick & Mencin are pretty explicit about how these observations have very limited utility for earthquake prediction, e.g., from Bendick & Bilham, "Global seismic synchronization has no utility for the precise prediction (in a strict sense) of specific damaging earthquakes" or Bendick & Mencin, "The most notable shortcoming of this outcome is that the empirical synchronization approach provides no useful constraints on the location of events in a developing cluster; they occur globally"

So in the end for both of these types of potential correlations (and any real underlying causation), the extent to which these provide anything actionable is unclear. I.e., does saying that the risk of an earthquake for all places, globally, already at a moderate to high risk for earthquakes are slightly higher on full moons help anything? Is everyone in a seismically active area across the entire globe going to do something different around every full moon as a result based on something like this? Studies like these are useful in the sense of working out all of the myriad controls on aspects of the seismic cycle, but their real world applications in the sense of forecasting are pretty limited.