Peroxide is bad to use on wounds, period. It damages live tissue along with dead tissue, is very irritating to surrounding healthy tissue, and just prolongs healing time.
The vet is not taking advantage of you, although the prices are a little high.
Unfortunately, broken toe nails are a large pain to deal with. It may seem minor, but when you think about it it's really not. I deal with them ALL the time at work.
When nails snap or break, it is usually close to the nail bed. This usually leaves the entire quick bloody and exposed. This is an EXTREMELY sensitive bundle of nerves and tissue. Think about how painful it is to break your nail. Now could you imagine having to walk on that?
These broken nails either need to literally be RIPPED off and out of the bed, which is hard on big dogs because that's a strong nail bed, OR if they're are snapped down close like the next picture, then the entire nail and quick literally need to be cut off down to the bed to promote proper healing.
So, could you imagine if you broke your nail, so I grabbed a pair a plyers and literally ripped off your entire fingernail? THAT is what we need to do when a toe nail is broken in a dog. So no, I disagree, it's not a minor thing.
To do this we need to sedate the dog. I've done it on awake dogs where owners refuse to pay for the sedation, and in my honest opinion that's outright cruel and cheap. I literally lay my entire body on your dog so the poor thing can't move so the vet can rip out his nail while he's awake. Do you want your fingernail ripped off while you're awake?
After sedation, we apply a bandage that allows for padding for 3-4 days while that quick hardens and becomes less sensitive. This is to prevent infection, but also largely to just provide comfort to the poor dog.
Cephalexin should not cause drowsiness. Could be his toe is extremely painful and he's sensitive to the pain. The average dose we use in emergency medicine is 22 mgs/kg
My Berlin would get 750mg and Zeke would get 1000 mg, because the capsules come in 500 mg and 250 mg and that is the closest way to break up the doses.