No, the pebbles do not move or recirculate a significant amount. They are typically static, they HAVE to be for the reactor to work. The fuel pebbles just sit in a pile arranged with particular geometry to allow the radioactive material to reach criticality. The only thing that recirculates to any large degree is gas around and through the pile of pebbles, which serves as the heat transfer and cooling medium. You just have a hopper and a hatch for reloading more fuel pebbles and removing depleted batches, and a screw mechanism that occasionally shifts some pebbles from the bottom to the top. It’s a lot simpler than you think. I work with pumps and mechanical seals IRL, the footprint for the gas recirculation system would not be that big. Biggest part in both terms of mass and volume would likely be the radiation shielding. If you want hard numbers for volume of the gas transfer portion, give me a gas flow rate and I’ll find a suitable system IRL that would handle it.
Edit: For the whole thing, I could give you a rough volume estimate if I knew how much power you want it to generate, and if I can find data to estimate how many pebbles you would need to initiate criticality, (to find the dimensions and reqired shielding thickness) I’m a mechanical engineer, not a nuclear engineer or technician, so it wouldn’t be 100% certain, but probably in the ballpark.