Bashir said in DS9: “In Purgatory’s Shadow” that the Breen didn’t have blood, but considering they never took off their suits, how did he know that? And if they don’t have blood, how does circulation work?

There are animals that don’t have circulatory systems, but they’re usually of a very simple order like sponges, nematodes and flatworms for example.

So either the “fact” that the Breen have no blood is misinformation, or they have something else that substitutes for blood.

Some invertebrates have circulatory systems which carry hemolymph, a fluid made most of water and contains various substances like carbohydrates, lipids, amino acids, etc. It’s not blood, but it still serves a circulatory function.

Maybe

I would posit that the Solid "face" Breen biology that L'ak is maintaining bleeds, while the transparent gelatinous one doesn't bleed, making the non-bleeding Breen the social norm.