Sun's rotation over time sort of aligns everything on that plane (or maintains momentum from accretion disk), galaxies are mostly also in disc forms. Pluto is a bit of an outlier, I wonder if due to some ancient collision or some other force.
So yes its a vast space (2D -> 3D), but should be rather empty no?
JWST has already challenged a lot of our perceived notions about the cosmos. Always worth checking more thoroughly and reexamining our theories as technology advances.
AFAICT most of the systems we've found with >1 exoplanet resemble our own system, where the planets are moving in roughly the same plane. If you look at this catalogue [0], the "i" value refers to the inclination of the orbit as viewed from Earth, since the parent star's rotation is often unknown. Still, it can be used to compare planets with others in the same system.
The closest I can find to your claim is some stuff from 2010 [1] (many exoplanet discoveries ago) claiming that a significant portion of "hot jupiter" setups are weird.
One theory is that interactions and collisions (all scales: gas, dust, comet, planet) are what cause the participants to align in the direction of the original net angular momentum, and the Oort cloud is just too sparse to that have happened as much.
Oort dust clumped up to comet-size objects for sure, but that tended to happen for the particles that were already roughly in the same orbit. Looking at all orbits in the Oort cloud, they remained more random.
So yes its a vast space (2D -> 3D), but should be rather empty no?