so here's what little we know:
- on the ever after side, the door goes through the tree; "the tree built them a special doorway to a greater beyond where the brothers could try creating worlds of their own…" – ergo, the door is part of the tree.
- within the tree, nothing can happen to you except what you want.
- in 'the girl who fell through the world,' alyx is depicted as a young girl who "flees the consequences of a choice to a magical place" – because her brother wrote the book to guide her and jaune home, and alyx herself alludes to the white rabbit, i think it's likely that what really happened is alyx ran away and lewis chased her.
- alyx and lewis grew up in pre-war vacuo under mistrali occupation, which is to say there were certainly some big things they might have been running to escape.
- the door would "remain open for the brothers' return and any of their creations," BUT not only can the cat not pass through the door, they're spiritually cut off from the tree altogether until neo's jabber simulacrums devour them.
- "for it is in passing we achieve immortality; through this we become a paragon of virtue and glory to rise above all, infinite in distance and unbound by death." <- my dead horse i know i harp on this incessantly but our souls transcend death.
the brothers lacked something – or withheld something whether on purpose or by mistake – and thus: the cat can't commune with the tree, the jabberwalker unmakes whatever he eats, and the mankind of the brothers' make had no magic of their own, only what the brothers deigned to give them.
salem is twice-drowned: first in the fountain of life, made infinite through her death-and-resurrection; and second in the pool of grimm, which destroyed and recreated her—unbound her. if she does indeed know the blacksmith, it'll be because she found the door in the depths of that abyss.
as in, when she sought freedom from her unending isolation, she found it. and found the means to remake herself. and remade humanity in her own image—the faunus, and humans with aura and semblances.
who are, or have the potential to become, in her own words, "much more than just a man."
…that to say, i think ozma is cut off from the tree in the same way the cat is. it's not a matter of having no attachments to remnant (as the cat believes) but rather of being spiritually bound – or closed off – kept separate. the brothers' mankind persisted after death in a state of unknowing stasis; they were either prevented or unable to join the natural cycle of death and rebirth.
ozma dies and comes back in the shackles of a curse that molds him to fit light's purpose. he alone of all remnant's people has not been freed, unbound in the way that salem and the humanity who rose from the ashes with her have been unbound. i think if ozma tried to go through the door he'd be bounced, just like the cat.
until, unless remnant's equivalent to the jabberwalker simulacrums—that is, salem—breaks him free. unbinds him. (the allusions to marvelous land of oz and the little prince points in this direction too: freeing ozma and oscar from each other is going to involve deaths-and-resurrection in some form, symbolic or otherwise.)
i also don't think he's ever found the door, because: that world just isn't as dear to me without her. and "as light fills my eyes/i'll picture me beside her/and pray that i inspire/i promise i'll be here until the end." all he's ever wanted is to be with salem, and as long as she walks remnant's face, ozma doesn't want to leave her. deep down, in his heart of hearts: "i promise i'll be here." and in the same stroke he feels no hope of escaping his curse and has become resigned to it.
if either of those things changed, i think the tree might open to him – but he needs to be unbound before he can hear it or see it or pass through it.