I think your instincts are right on the money. I'd let him be for now. Keep him in the carrier he started to make an improvement in, continue the talking, petting, and I'd keep the other bunny out of his vision.
I agree that it's not over yet.
When they get that shaken up, it takes a little bit before the eating and drinking comes back. With his stress level, you want to keep an eye out for Stasis because this could've weakened his immune system a bit if the eating/drinking and pooping doesn't start, but for now, one thing at a time.
Since you've given him some vegetables, might consider a piece of fruit too, that has water in it and so hopefully he'll have a nibble here or there. At least he took a sip of water.
It's encouraging that he's coming around. You're doing a wonderful job.If there's a way for you to monitor how much he's drinking do so.
Rabbits won't eat if they're in pain. That's why at some point, we really need to be sure that he's had a good check over for any scrapes. They will fight until they get tuckered out, then rest, and they'll resume the fight when they're feeling stronger again. I don't know what time the fight could've started between the boys, but it may not have been just one. It could've been a couple depending upon when the break-in happened.
For tonight, I'd just keep talking to him, petting him, offering him anything he wants, and keep him in a quiet area.
Prayers continue.
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ray:
-Carolyn