Yes, the probability of tsunamogenic landslides do increase during earthquakes, but it's still quite unlikely for an event of this magnitude tens of km from the continental slope; this is why a properly-calibrated tiered system would be better.

The reason that the Palu event is so notable is precisely because it's uncommon. It's also a very different system: the causative fault is running along the axis of a shallow bay that is only a few km across, so even if the landslide did occur, rapid movement of the steep, shallow coastlines would surely have generated a smaller tsunami. It's a geographical and tectonic situation in which at least a minor tsunami is expected a priori conditional upon an earthquake, so a warning system would account for that in principle. (In practice there isn't time enough to mobilize because the tsunami hits while the ground is still shaking). The bay at Palu is like a somewhat larger Tomales bay--an earthquake right there is going to make some waves. Very different situation than one far off shore.