I think you can approach this in a fairly simple principled way: what are the consequences of the character's disability?
Most of your question describes there being no consequences at all. If it's true that the character has a choice of two worlds, and literally the only difference between those worlds (for them) is that they walk in one and use a wheelchair in the other, then sure, I find it believable they might move full-time to the one where they walk. Especially if they acquired this illness rather than being born with it, and/or they are fundamentally avoidant of its reality.
However, I agree with you that this is a very shallow representation of disability: if a fictional tree falls in a fictional forest and nobody writes about it, does it make a sound? If there are no consequences whatever of your character's disability, and it has no effect on their quality of life, then are they really disabled? It's more like someone who doesn't like their home town so they never go back there, than it is like someone living with a disability. It's believable, but it's quite the cyberpunk cliché: "reality sucks so I don't go there much".
Furthermore it's also wholly believable that they they wouldn't live fully in the dream world, or that they'd stop doing so after a time. Maybe they (in common with most people with disabilities) don't see their disability as the end of the freaking world, or at least most of the time they don't think that way and don't find life utterly unbearable. Maybe there's something in the "real" world that is worth having that can't be had in the "dream" world - it's your job to decide and to put that there. Maybe they are otherwise forced by circumstance, society, or events, so they have no realistic choice. Maybe if they don't spend time in the real world, the illness progresses faster and they die (for a reason, I mean, like they're treated in real-world. Not because their illness is, "allergic to dream-world". Unless you can make that work).
If they're a/the protagonist in a novel, then pretty much by definition they are going to have to do some things that they don't really want to do. At least initially, as they are or appear at the start of the novel, they will not want to do them. A couple of shoves and some character growth will soon change that, though. They might try to resist doing them, but it ain't going to work. Even as a secondary character, it's not a bad idea for them to face some kind of meaningful difficulties. So, it doesn't really matter what they think, does it? They're going to have to deal with the "real" world at some point.
Fundamentally, I have no disability and I don't seriously compare this to a disability, but: I do have my house set up pretty much how I want it. It's great. I still choose to leave the house. People with disabilities, far more so, often have their houses set up to be way more comfortable and convenient for them than most of the rest of the world is. They still leave the house, in huge numbers, for a whole host of reasons ranging from: they want to, through to: they have to in order to continue living.
Just don't act like the "solution" to disability is for it to magically go away at the end. Either this is a character who lives in dream-world, with the minor quirk "can't walk in real-world", or it's a character living in both worlds who has a genuine and unavoidable disability in one of them, which you can address in a way that's respectful to non-fictional disability. That said, obviously some illnesses can be cured and some conditions can be treated, so nothing's out of the question.
I imagine probably there's a trap in assuming that it's "natural" to want to avoid the disability by staying in the "dream" world, or "natural" to want to embrace the disability as part of the character's identity and hence cling quite strongly to the "real" world. I don't think either is correct, and different people have different views about their disabilities at different times, but on the whole I get the impression that the desire to be "cured" (and I use that term in snigger-quotes for disability in general even though it applies to many illnesses) is less universal than I might have naively imagined.
If you are not disabled yourself and aren't in a position to even begin to know what's OK and what's not, then you aren't writing from that POV, and you almost certainly won't represent it accurately. Maybe with a lot of research and listening, but pretty much forget about it. Likewise, I can't give you permission to write it: at best only your readers with disabilities can do that. The fact that this character can get a rest from managing their disability "any time they like", yes, that's going to take something away from the portrayal, since most disabilities don't work like that. But the alternative is to write a whole lot of characters all exactly the same as you, so I think you kind of have to give it a go and see what happens.
Note that you can always use test readers, so you can ask people not, "should I try this?", but "I tried this, here it is: is it OK?". If it's not OK, change it or scrap it.
Just noticed you require an example. Unfortunately I haven't seen it yet, but at least include CODA. I'm pretty sure it's mostly "OK" since although it clearly got some things wrong (which you can read about online) and a lot of Deaf people have raised ways that it's unrealistic, I haven't noticed any furious boycott-storm. The general narrative seems to be that it represents some degree of progress, and that where it misses people seem to accept that's due to honest failure rather than fundamental disrespect. Also, I think many Deaf people experience a world in which everyone in their own home signs, and so the effect on their communication really is very different indeed in some places than others. I wouldn't take it as the last word on how Deaf people live their lives in America, and an assessment from Lennard Davis is particularly striking: "this genre of films is glued to a different reality: it is as if birds were obsessed with making movies in which humans were miserable about their inability to fly." But it definitely plays with a version of two-worlds, so why not look at it and learn from what it does well and its shortcomings?