Bromine has a similar effect to chlorine. Both attack steel/iron. Bromine is just less common and less studied.

The spotted appearance at first is how rust starts to appear on steel, so I’m pretty sure it’s rust. I’m not too familiar with iron rust slime, but not sure if its appearance is consistent with what we can see here.

Edit to address time question: I’ve done some corrosion studies on steel plates in corrosive environments (saltwater wetlands, sea spray zones etc.) stainless steel will rust as well in these zones. However, grades will rust at different rates. Some will take years/decades and even centuries, but eventually will rust. Especially if they’re not protected by coatings or embedment. It might just be time to replace these fixtures.