"a higher dimension"? If you mean to suggest that our reality is like, a (3+1)D slice of something bigger, I don't think we have much reason to suspect that, and, even if it were true...

Well, ok, I suppose maybe we could construct some kind of vessels in this larger space which could like, well, if mind-uploading is achievable (or, even if just mind-transfer-to-a-new-medium is possible) then conceivably we could do that to be able to live in such higher-dimensional space?

But, unless it granted us more control over our environment in a useful way, I don't see why that would be particularly desirable? Well, I guess it probably would grant some more control, but like,

our minds, I think, are suited for the kinds of experiences that humans have generally had, not so much for, whatever constructed bodies we might somehow build for such a higher-dimensional space.

I don't mean like, "our minds aren't well-suited to navigating in higher-dimensional spaces, with higher-dimensional sensory-input". That might be true, but maybe we could adapt to that part without too much of an issue, idk.

Rather, I mean stuff like, it is important that we have things like, the feelings of sharing a meal with one's loved-ones, hugs, and other physical expressions of affection. (I am not making the claim that hugs are a human cultural universal. I don't know. But I'm fairly confident in my assumption that all successful human cultures have some form of physical expression of affection.)

Now, I'm not saying that such things would be inherently impossible with more dimensions of space. Why would they be? But, I'd imagine that even if our minds can adapt relatively easily to piloting a body in a higher-dimensional space, that, probably the combination of our minds and whatever bodies we constructed for navigating such a higher-dimensional space, and the kind of larger-environment that there might be in such higher-dimensional space (I imagine it being fairly desolate, as if there were things living there we would probably be toast already) would not be conducive to having those experiences in those bodies.

If you mean more generally, "some true-er view of reality" and not necessarily "higher-dimensional space" (but still in a way that differs substantially from reality-as-we-currently-perceive/experience-it)...

Well, sometimes I imagine that heaven might not operate like (3+1)-dimensional space (perhaps not corresponding to any kind of smooth manifold). In this case, I would imagine that this would be fine (by assumption of it being "heaven"), because either we would always have been designed so as to be compatible with it, or it would have been designed to be compatible with us, or both.

(side note: If I had to guess, I think my current guess is that heaven does actually, at least sorta-kinda-in-some-sense(not that I have an idea of "in what sense") be spatially 3D, or resemble that in some way. But, I'm not confident either way.)

But, if we are working under the assumption that reality doesn't hold those-we-would-regard-as-people as "special" in any way, such that we would have particular reason to expect it to be good to us outside the scope we find ourselves in currently, then, I would generally not expect this this "higher reality" or whatever, to be well-suited for us.

Maybe it could be exploited in some way, to make things better in this portion/view of reality, and maybe more parts could be made to be like this one, but, under the assumption of an uncaring universe, I would expect that any "higher/true-er reality" would not be really nice for living in.