The Bug

Possibly related to MC-279402

According to the changelog of 25w02a, farm animals are supposed to spawn in Badlands biomes now. 

It seems, however, that they only spawn in Wooded Badlands. And even then, very rarely. Generally the biome has to be larger than average Wooded Badlands generations to get any spawns.

Initially, I thought this was because of Wooded Badlands having grass. Perhaps the intent wasn't for farm animals to spawn in normal Badlands despite the changelogs implying otherwise. Only technically spawning in wooded badlands, but able to spawn in the other Badlands biomes if grass was present.

This isn't true either, however.

After killing all entities, creating a huge plane of grass in a Badlands biome, upping the tick speed and letting it sit like this for a few hours, absolutely no farm animals spawned. So surely, this meant farm animals couldn't spawn in badlands at all despite the changelog's mention of it, even in grass?

Well it seems that isn't true either.
The only situation where I was able to get a farm animal to spawn in a non-wooded badlands biome was in a superflat world.

But in a normal world, this doesn't happen at all, even in the presence of artificially placed grass. And even among wooded badlands, it seems to be quite rare.

Conclusion
I'm unsure what the intentions of mob spawning in Badlands is. The changelog made it seem like they'd be spawning in average run of the mill Badlands biomes, but aside from in a superflat world, they don't seem to at all, even in the presence of grass. They DO spawn in Wooded Badlands, but it seems to be quite rare and not happen in an average Badlands, only in the very very large ones with lots of Wooded Badlands present.

Again, combined with MC-279402. something about the new mob spawning in Badlands biomes seems to be a bit off.