Don't touch it just keep doing what you've been doing.

But I'm afraid the roots may dry out and wilt away before they reach the soil.

Yes, they may dry up. But those are air roots and while they could possibly grow into 'soil' roots, they are OK to dry up. As you can see, there are air roots growing from juncture of other segments too. Those will never reach soil - too far.

To root your cutting properly, it will grow roots from the end of segment in the soil.

Yeah, sorry JeffO, but really, you're kinda of confusing things. When it comes to giving advice, respectfully, your conjecture above is incorrect & I think to newbies confusing. Really isn't helpful.

Perhaps here too, one might consider when it comes to giving advice, when in doubt don't.

These plants are tropical jungle cacti, & they grow aerial roots normally, that's what they do, sometimes they dry out & sometimes not & the plant is fine (as Rina suggested). Not necessarily searching for water, sometimes trying to anchor the plants, since in the wild. they grow in crotches of tree branches, not even in soil.

Your cutting would do better in a plastic pot, after having its mix changed to equal parts Cactus & Succulent mix or African Violet mix & Perlite.

Sounds like maybe you're new to plants, pls. don't be so scared, the plant'll be fine.

The post is rather ambiguous. If it is a rooted plant, Jeff is right that it is showing signs of dehydration. If its a cutting being rooted then it's a normal appearance while roots get established.

Also, if it is a dehydrated plant then the soil could be too wet or too dry. It depends on the conditions the OP has been keeping.

Edited: I deleted a couple of my comments because I misunderstood the OP. Sorry for any confusion.

Just wondering what putting the cutting in a plastic pot would change?

Schlumbergia grow in the wide spots on trees and on the ground, with the branches often lying prostrate on the ground. Aerial roots then are quite near the ground allowing the plant to extend its length.

Update: the plant is now rooted in the soil and is looking a lot healthier, still no new growth though :(

Update: Finally some new growth has appeared!!! Today is the first day I’m noticing it. Looks like the plant is doing well still, hopefully it will continue to grow!

What a relief. That's so nice to see. Maybe you could report back if they flower this fall.

Update #3: Over the past few days I have been checking on all my plants and noticed this one has outgrown its pot! There were just a few roots starting to come out the bottom. So I decided to repot it into a bigger plastic pot. Hopefully I won’t have to repot it for a while now.