Injectables mainly here which seems to be permissible by “organic” standards-I see no difference between giving antibiotics in shot, feed or water. Most are a sulfur compound or a penicillin type-both found in nature.
Seed, here is an excerpt of what I found when checking on antibiotics and organic dairy in the US. And a link of course. Using antibiotics are required in certain circumstances but that animal is no longer organic. They have to sell it as non-organic. Some write-ups on what constitutes organic aren't real clear about whether or not the animal is still considered organic, I've seen some of those and can see why you said "seems to be permissible". This is specifically for dairy but it is pretty clear.
Use of Antibiotics
In an emergency, a producer must use antibiotics if necessary to save the life of the animal or to prevent suffering. Use of antibiotics should be based on the recommendation of a vet. Withholding treatment of antibiotics from animals to maintain their organic status is prohibited.
If a producer uses antibiotics, they must do the following: Record the event in their health records. Notify their certifier of the situation. Segregate the animal to prevent contamination of organic products. For example, a dairy cow must be marked to prevent the milk from going in the bulk tank. In addition, the milk may not be fed to calves. Sell the animal to a non-organic market. Document the sale of the animal.
https://www.ams.usda.gov/sites/default/files/media/Dairy - Guidelines.pdf
As far as using composted manure, if you know where the manure comes from you know where it comes from. If you don't, you don't. I'm personally comfortable using thoroughly composted cow manure, I figure those drugs have broken down through the composting process and are no longer present, at least not in harmful quantities if at all. But if you are not comfortable with that, don't do it.