All bottle neck brass is annealed. Ya annealer multiple times actually during the manufacturing process. It has to be in order to form properly without cracking or splitting. It gets a final induction annealer before the final sizing to form the neck and shoulder.
Most manufacturers used to polish the brass after all the annealing and sizing to make them look really nice.
It's since become increasingly popular to not polish the brass after the final anneal so that the discoloration remains. People have come to like seeing that. Military spec brass requires it to be there. I think that's how the trend started with commercial brass.
Either way, some people have gotten the wrong idea thet not all brass is annealed and that only those with the discoloration are actually annealed. That's completely false. All of it is, rest assured. Lapua and many of the other top tier commercial brass manufacturers do not polish the discoloration off and others like Hornady, Nosler, etc polish their brass to remove it. That's it.
The discoloration is mostly from contaminated/residue on the brass itself causing a reaction under heat. Completely clean/raw brass will barely discolor at all.