I don't buy meat from anywhere you can give healthy livestock antibiotics, period. It's really easy (obviously in case you live in such a country you'd be forced to not buy meat or buy imported, which is more expensive and worse for the environment).
Not sure about the definitions about prophylaxis and metaphylaxis but I was under the impression any systemic use of antibiotic use in healthy animals was outlawed e.g. in the EU.
There may be local regulations or labellings to (e.g. some organic labeling means no antibiotic and so on). But as a first rule I just try to avoid meat from "bad" countries. E.g. we get quite a lot of imported Brazilian beef in stores and I know it's terrible both for deforestation and antibiotics so I avoid that completely. Some interesting differences in the map is e.g. between Australia And NZ.
There's some devil in the details, of course, are the antimicrobials used in animals the same as those used in humans? ie. Does increasing resistance in animals to X product result in resistance to Y product as used in humans?
Sheep are pretty easy keepers. They need less hands-on care than many other livestock (other than shearing, which produces wool that can be sold), they don't require shelter, they don't require strong fences, they don't require high-quality feed, etc.
There can also be other forces at play. For example, we have just transitioned from la Nina (which brings high rainfall to this part of the world) to el Nino (which brings drought), so a lot of farmers will be downsizing their flocks.
Changes in wool prices can also affect lamb prices.
Luckily for me I can just avoid buying imported from bad countries like Brazil. All imported from good countries AND all local meat is ok (because I live in one of the good areas on the map). If I did live in (say) Poland, it would be harder and more expensive, but I'm sure it would be possible to avoid buying domestic, and it wouldn't necessarily be that much less sustainable. At least not compared to buying things imported from a different continent.
> In January 2022, the routine use of antibiotics was banned in the EU, and preventative use was restricted to exceptional treatments of individual animals
EU law is pretty strict about labelling meat coming from the EU/outside the EU so that could be one way.