(Yawn)
You're boring us.

Right. Kind of weak and circular.  What's the definition of "empathy"
in this context?

Here's my take on it, FWIW.  I am not an anthropologist.

Humans are social animals, like chimpanzees.  For millions of years, we
hominids all lived like chimpanzees in extended family groups as
gatherers with some hunting.  It's useful for such groups to
synchronize their activities.  For one thing, it keeps them together
for detection of and defense against predators.  So if everybody
settles down for the afternoon nap at the same time, rather than
wandering off foraging individually, and everybody gets up looking for
a snack at the same time, it's safer and more efficient.

It would support my offhand theory if the observed contagious yawning
in chimps resulted in the group all settling down for a snooze or
louse-picking session together.

Btw, anyone who has looked after house cats will have observed that
their vomit smells no different than their food, while the smell of
human vomit makes most people want to retch.  While cats are solitary
foragers, who eat mostly fresh-killed meat under natural conditions,
humans are group foragers who eat almost anything.  If one gatherer has
eaten a toxic plant or some badly spoiled carrion, most likely other
members of the group have too, and if one member vomits, it's adaptive
for the others to as well, before they get as sick as the first guy.
Hence contagious vomiting.

I wave my hands and speculate that the human stomach secretes some
chemical in minute amounts that the human nose is extremely sensitive
to, the smell of which stimulates emesis in humans.  Perhaps some
strong-stomached or weak-nosed researcher has identified this substance
already.  I'd expect the military to fund such research.

Btw, I wouldn't describe the feeling of nausea I get from seeing,
hearing or smelling somebody else vomiting as empathy, ditto the urge
to yawn when everybody else is, but maybe a non-human student of human
behaviour would.

I'll back off before I sound any more like Archimedes Plutonium.