First time dog owner here so this might be a silly question, but sometimes Appa seems to be breathing like he just came in from exercise even though we've been in the house relaxing for quite awhile.

It doesn't last long, maybe a minute or two, then his breathing resumes back to a slower pace. I'll try and video it next time it's happening to see if that helps.

Is this normal?

Is it panting or just rapid breathing? If it is panting, even for a short while, it is probably Appa's way of controlling her body temperature. Miko has done this since she was a pup, I asked the Vet about it because it happened even when she was lying down. The vet explained that just like humans a dogs body temp increases when they are sleeping. Panting is like sweating for dogs. If your not sure feel Appa's nose. When miko is sleeping her nose is always warmer and drier.

if it's panting, it's sometimes a sign of stress. the first few nights we had Zoey home, she was a little over 4 months, she would pant and pace a lot

Becky wrote:

If your not sure feel Appa's nose. When miko is sleeping her nose is always warmer and drier.

Yep, Mya and Kody both pant before falling asleep. That's how I know that they are sleepy. They're noses are also pretty dry when they're relaxing or sleeping.

Sierra will bust out loud breathing while just laying around, it does not last long and i don't think much about it.