Animation can get stuck currently, do not move to much at the same time else you cant break it, but if your encumbrance is not to high then you can break the stuck animation by jumping, you should stil regain stamina over time but this is slower in "tired" then in normal or sitting mode.
I've tried everything when I'm stuck in the "out of breath" mode and nothing will break it.
As the last screenshot shows, I was not encumbered at all, it was purely exhaustion from fishing, yet I was still stuck that way and unable to break it except with relogging (which takes 10 minutes or so)