If you have villagers gathering from deer near a mill and you move some sheep nearby the villagers will not automatically start harvesting the sheep after the deer are depleted.
I think they will only gather from the sheep if they are dead already, but they won’t kill them on their own once the deer are finished.
On top of this, there seems to be some strange behaviour when villagers finish gathering animals. When the villagers go idle there is a big delay before they appear as idle villagers in the taskbar and they do not have the “Zzz” animation above their heads. They will also automatically start gathering again if you drop a deer nearby even if they have been idle for 30 seconds or more. It’s like they never really become idle and instead just stay in a paused state.