It’s actually quite intuitive, as the force is distributed over a larger area. So although the pressure gradient isn’t affected by the discontinuity in the container size, if you compare forces exerted by the pressure on a plate in either section of the chamber you’ll observe that the force on the wider plate would be reduced to compensate for the increased area in the presence of the same pressure.
I'm not sure why you're being down-voted. If you double the size of a water column, you of course double the total weight pressing down. But you've also doubled the cross-sectional area, so the weight-per-unit-area (pressure) remains the same. This is pretty intuitive if you understand what pressure is.
Perhaps because the explanation (and indeed concept) isn’t that intuitive so the comment may be read as dismissive?
If you see pressure as coming from the weight of the fluid above and now replace fluids with solids for a mental model, it obviously doesn’t work: imagine two parallel rigid plates connected by some rigid structure. The top plate will represent the (fluid) boundary between the top of the barrel and the tube and the bottom plate the bottom of the barrel. If you put a narrow column of metal on the top of the top plate, then the pressure exerted by the bottom plate is, say, p. If you make that column much wider, increasing the weight above, the pressure is say 10p.
I think the problem is that this intuitive model of pressure is just wrong but if it doesn’t come from the weight of the water above, it is hard to intuitively see where it does come from.
Your example is completely different though. Considering neighboring water columns isn't like adding more to the top of the plate, it's like setting up an entirely different plate next door. Which of course doesn't affect the first instance at all.
The point is that the way people typically think of the problem leads to examples like mine, and this is why the concept is unintuitive. It doesn’t matter whether the model is correct—the whole point is that it is the incorrect model many people will have or start with.
