The phrase nine worlds appears in the sources, and no source lists them. Every enumeration a reader has met, with Asgard at the top and Helheim at the bottom and seven in between, is a modern reconstruction assembled from names scattered across the poems and Snorri's prose. The names are genuine. The tidy diagram is not, and where the tree, the worlds and the bridge sit in relation to each other is inconsistent even within a single text.
Asgard itself is described mostly through incident. It has a wall, built by a giant who was cheated of his fee. It has halls with names, Valhalla and Gladsheim among them, and Bifrost reaching it. Whether it stands in the sky, in the branches of the tree or on the same plane as Midgard depends on which passage is being read.
Snorri complicates matters further. Writing as a Christian for Christians, he opens the Prose Edda with a prologue explaining the gods as men out of Troy who were later mistaken for gods, and he glosses Asgard as Troy itself. That framing let him record the material without endorsing it, and it is one reason the Edda survived. It also means the single most complete account of Norse cosmology was written by someone arguing that it was a misunderstanding.