They are vertical cylinders to be suspended vertically in a pool of water, not massive squat objects sitting on bedrock. They are thin and relatively top-heavy. It is not ludicrous to ask what could happen should they not remain as vertical as designed.

From a planning perspective, if verticality is a requirement then that verticality has to be protected as strongly as any other aspect. Any attachment or mounting points that maintain verticality must therefore be earthquake proof. If, as in the pictures, these reactors are held in place from the top, horizontal shaking from even a small earthquake would put massive strain on that joint. It isn't just the long/thin/heavy reactor but all the water sloshing around too. A super-strong joint and maybe something important bends/breaks under load? A flexible joint to allow the reactor to sway? Sway how much? What happens at the travel limit of the joint? Can we risk the reactor contracting its neighbours? These are not trivial engineering questions.

I think they are not trivial but relatively easy parts of the design. I’m sure they can design support structure to withstand whatever arbitrarily large earthquake you throw at it. The structure doesn’t need to be particularly light or compact so there shouldn’t be any design constraints getting in the way of strength. The heat transfer problem is much much harder and they’ve already solved that apparently.

I;m not saying it is impossible, just interesting. One option could be to suspend these reactors on cables from above. That might let them swing around all they want during even a huge quake. The water would act as the dampener. Not much extra engineering required.

I was assuming they'd bury these.

As other Nuke submariners in this thread can attest, there are definitely PWRs designed to tolerate massive rolls and “angles and dangles.” I guess it depends on your definition of sideways.