They definitely pick up on our emotions. My boy bun will run away from anyone who is stressed or feeling negative. SOMETIMES if I’m really sad he’ll stay and cuddle, but only if I’m really sad. If it’s just a bit he’s like “see you later when your better!”. If I’m in a good mood, he’s so happy to see me and cuddles a lot. My girl bun is a new addition, but so far she doesn’t run away when I’m stressed, she’ll stay beside me to be pet and calm me down. She’s still getting used to her new home, but when I was sad she stretched out beside me for the first and only time, which made me happy that she’s starting to trust me more. They notice it, but their reaction depends on their personalities.
They pick up on a lot of things. If I’m lightly stressed by say something that happens in a tv show (like suspense, etc.) they will stand on guard and scan the room to see what is stressing me out. If I don’t like someone, they don’t either.
My boy bun can even tell kids from adults (even the bigger kids like 13-14). He acts completely different and will tolerate a lot that he never would from an adult. They often pet him weird or too hard (before I tell them how to), but he’ll stay and come see them. With adults, he’s much more wary and won’t come see them. He’ll observe and stretch himself out to get as close as possible without moving his feet, but that’s it. It’ll take him at least a day to accept pets from new adults, but with kids he comes right away.