I was mistaken.

Our solar system is flat.

Galaxies are mostly flat.

But the universe is not flat. Galaxies are all over the place.

So, I was mistaken.

But, just to be clear: I am not a flat earther! Flat is relative here. The thickness of our galaxy is not measured in kilometers ofc. It is just that within the same units , solar systems and galaxies are flat relative to their length.