Baby zebra finch twirling...

[MiaCarter]

That video definitely provides some good insight.

I saw a lot more of the apparent dizziness in this one.

The near-constant head movements are worrying. That makes me think seizure (and seizures can be brought on by excitement or physical exertion, like begging.)
But it's hard to say. I suspect it may just be an unusual presentation of twirling and the head movements are just connected to his begging tendencies.

The near-constant head movements are troubling for a second reason too. He's expending a lot of unnecessary energy, so that's going to explain why he's so behind his siblings in terms of development. His body is not only fighting an infection but he's also expending lots of energy from the head movements.

What's odd is that when my zebra finch had twirling and the handful of other cases I've seen, the birds tended to put their wings out for stabilization. I don't recall seeing him do that.

I noticed you have a mug with water.
I would definitely eliminate that until he's 100% recovered.
I could easily see him falling in there and being unable to get out. I can tell you're fond of the little guy and I'd hate to see you lose him to drowning.

I'd ensure that all waters are shallow enough so if he fell in, his head would be above water and he could get out with relative ease. He'll be at highest risk as he starts to recover as he'll start trying to explore, but he won't be 100% yet and that will leave him vulnerable to that sort of accident.

Drowning is the #1 risk to birds with epilepsy or any other condition like this where they can't control their body properly.

I'd also give him a heat lamp. Just a simple gooseneck desk lamp with 40 or 60 watt bulb works great. I think I paid $4.97 at Walmart for my lamps. Put it right up against the cage and shine it on the floor in one of his favorite spots. That will help keep him warm, so he expends less energy on heating and more energy on growing. (Plus, you'll want to have one on-hand for any time they look unwell. A heat lamp alone can sometimes give them the extra boost they need to recover on their own.)

I'm glad you're going to the vet. Hopefully, it's someone who's familiar with birds? (Even so, an inner ear infection and twirling are two super common conditions that any vet with a degree that's worth the paper it's printed on can handle.)
If you're sent home with antibiotics --- and I suspect you will be --- I would also inquire about an antifungal med like Nystatin/Medstatin. This not only treats one potential cause of twirling, but it can prevent yeast infections. These babies are VERY prone to yeast infections without antibiotics killing off the good bacteria that keeps this fungi in check. If it's a vet who's not super familiar with baby birds, then he may overlook this. So be sure to inquire about it. (I always make a list of symptoms, observations and talking points so I don't forget anything.)