The Milky Way

The Pythagoreans held that the abode of souls is in the Milky Way, and they transition to earthly existence through the intersections of the galactic and ecliptic planes.

I think this simply refers to switching from a greater world to a lesser one. The ecliptic plane is the realm of the solar system, where the Earth orbits the Sun. The galactic plane is the realm of the galaxy, where the Sun orbits Sagittarius A*. If the Sun is a god, and the Sun is an inhabitant of the galaxy, then it stands to reason that the galaxy is the home of gods. Whereas we, here, in the solar system, are less than gods as we are ruled by a god.

So to reascend the planetary spheres to the fixed sphere and to regain residence of the Milky Way is to grow from our very small world, here, to a much larger one, There.

I don't think this is literally what happens—souls don't float around in outer space, I don't think. It is simply a symbol, though a surprisingly sophisticated one indicating understanding of what the Milky Way is and how it works, of the soul growing beyond its need for a bodily crutch.