Eberron setting has its own, particular cosmology.
The figure in the section Planes of Existence (Eberron: Rising from the Last War, ERftLW) clearly states the planet Eberron is in the material plane, but at the same time it seems to be not the Material Plane: indeed, there is a sentence that explain the uniqueness of Eberron setting (emphasis mine):
The planet of Eberron is the heart of its own Material Plane.
The initial paragraph of this section states that it is part of the Great Wheel1 of the universe, but at the same time
it is fundamentally apart from the rest of the Great Wheel, sealed off from the other planes even while it’s encircled by its own wheeling cosmology
This seems to imply that Eberron lives in a different material plane, because of "own" in the quoted sentences. Together with the second quote provided in the answer, it seems that Eberron setting takes place somewhere in the Great Wheel, it shares some characteristic with other cosmic systems but it has its own rules and place.
Eddy, very interesting, but is it on the Ethereal Plane or what?
The information seems to be contradictory, but the same figure cited above shows that the Ethereal plane surrounds the Eberron's Material Plane, following the rules of the DMG (page 48).
A weak escamotage to solve this issue could be adopting a different reading of the quote in the question: the three dragons were in the Ethereal plane when they were creating the cosmic system:
The three progenitor wyrms worked together in the depths of the Ethereal Plane to form Eberron and its planes as a new cosmic system.
Can the Dream of the Blue Veil spell allows to travel to Eberron?
In the section Eberron and the Multiverse one can read (emphasis mine)
It is theoretically possible to travel between Eberron and other worlds in the multiverse by means of the Deep Ethereal or various spells designed for planar travel, but the cosmology of Eberron is specifically designed to prevent such travel, to keep the world hidden away from the meddling of gods, celestials, and fiends from beyond.
Hence, since Dream of the Blue Veil spell is designed for planar traveling and there is at least a Material Plane on Eberron, such spell can be used to go to Eberron. Note anyway that in the same section of ERftLW we can read that a DM could rule that the barrier formed by the Ring of Siberys is intact, and it is not possible to reach Eberron and its own system from other worlds:
In your campaign, you might decide that the barrier formed by the Ring of Siberys is intact, and contact between Eberron and the worlds and planes beyond its cosmology is impossible. This is the default assumption of this book
1 Aiming to generate more confusion, in the DMG, page 44, one can read about different cosmological system other than the Great Wheel, the World Tree and the World Axis. Among them there is The Orrerey:
The Orrery. All the Inner and Outer Planes orbit the Material Plane, exerting greater or lesser influence on the world as they come nearer and farther. The world of Eberron uses this cosmological model.