I'd always suggest you separate the bully, if just one chicken is attacking; you already did and that's a good idea.
The bully is clearly excessively aggressive. There may or may not be something wrong with the one it's attacking, but either way all your chickens are at risk if you keep a chicken among the flock that takes it upon itself to attack others with intent to kill, which is what it sounds like to be honest.
Since they are so young, I don't think it's at all likely that it's trying to weed out a sick or hurt flockmate as the popular notion goes. Only adults do that, pretty much as a rule.
Instead, it's just mentally abnormal. Which is very common unfortunately, common enough to be normal really. But normal isn't natural, though people often think anything they do is therefore natural for the species despite how much we've altered their physiology and society.
Generally, raising chicks under their mothers makes for more calm societies, raising them artificially makes for tamer chickens but they're more likely to have some social issues and conflicts between themselves. They're a family bird and males and females raise chicks together in the wild, both teaching them how to interact, and when they become adults keeping them in line and making sure they mind their manners. This doesn't happen with chicks raised without a mother, and most domestic roosters have no fatherly instincts anymore anyway. But having mature hens and roosters around can do wonders for the social order of chicks, helping prevent social issues by promoting tolerance and keeping the order.
Most of the time people assume there's something wrong with the chicken being attacked, but most of the time there's actually something wrong with the chicken attacking. They're not wild animals, humans have done much to breed many instincts out of them or alter them, so their instincts aren't always correct anymore. Extreme aggression is one common fault. So is cannibalism and it's possible your little Sebright is a potential cannibal. In that case upping the protein intake might help, but that mentality is always a risk to the others. If one should bleed, it could go into a feeding frenzy. Cannibalism isn't normal either, normal chickens will starve to death without attempting to commit cannibalism; it just never crosses their minds. It's a trait developed in some lines mainly due to intensive caging practices and it is heritable like most mindsets are. Major commercial poultry producers weed that out of their lines now. Before they used to just debeak but that is disallowed in most places now. It only takes a few generations, 7 as a rule of thumb, to breed a trait in or out.
In the wild they'd most likely leave sick or injured chickens to die, not kill them, since killing them is very slow and bloody business and raises the risk of making them more vulnerable to predators as well as catching whatever contagious diseases their victim may carry and thereby also taking themselves and their aggressive genetics out of the genepool.
Killing the sick/injured, or just killing other healthy chickens is something some domestic chickens do and it's due to how some family lines of some breeds have been kept, and how the selection of breeding stock was done (or not done). It's often very, very strongly heritable and tends to trend towards the worst, I don't know why though. Meaning that breeding an individual with mildly bad behavioral traits tends to produce offspring with worse traits, and the offspring tend to produce offspring in turn with even worse traits still.
If you want to develop a calm, safe, happy flock that doesn't bully, mutilate and kill one another, you need to weed out bad mentalities. They can and will make life a misery for all the others, and only be miserable themselves if you separate them permanently because they're social animals. Unfortunately bullies are only 'happy' with victims to hurt. Because the Sebright is so small, I would have thought maybe you could cage it with a much larger chicken, but that clearly isn't working for the victim. Maybe cage it with an older chicken that won't tolerate being bullied, if you want to keep it?
I would cage the Sebright separately --- permanently --- or rehome it, personally. Though it will likely be a liability to anybody else's flock as well, so really, I'd probably eat it, small as they are, but I understand that's probably not on your list of options as someone that's new to chickens.
Having separated your bully overnight, it will now have fallen lower in the social order, and when you reintroduce it, it may be more focused on regaining its status than bullying the other, but that tends to work more for adult bullies. It might put your little bully on the back foot for a little while though.
But pretty much as a rule bullies are just bullies for life, sooner or later it will be almost guaranteed to get stuck into another chicken.
Anyway, good luck with it.
Best wishes.
