This is a simple question to answer by looking at the definition of what an animal is, and what yeast is biologically.
Yeast is a class of single-celled eukaryotic microorganisms, a fungus. They are incredibly small, typically between 3-40 µm in diameter.
Animals are multicellular eukaryotic organisms.
Because yeast are not multicellular, it’s clear that yeast are not animals.
Can Vegans Eat Yeast?
The simplest definition of veganism is to not use or consume anything that involves or contains an animal.
More generally, vegans don’t eat things that are an obvious result of suffering.
Yeast does not have any semblance of a nervous system, and can’t feel anything, let alone pain.
So while it is “living,” in the same sense that healthy plants are living organisms, it is not capable of suffering, and we can be sure of that.
So, vegans can and do eat yeast of all kinds (brewer’s yeast, nutritional yeast, etc.) with no hesitation, so enjoy your bread!