I've been thinking about the idea of autism and lack of empathy. It's often cited as a key distinguishing characteristic of autism--an inability to empathize with others or understand how one's actions can affect other people.
Does your child show empathy?
Mine does, but it's erratic. He's also 4, and NT 4 year olds may lack some empathy from time to time. Last night he had no clue that I was angry with him over his behavior. I had to walk away from him to get his attention actually, before that I was starting to yell and it made no impact (I know not a good reaction). Leaving him alone often gets his attention.
But then there are things that make me think he understands it a bit. He often picks me flowers because he knows I love them (this is what he says). One boy in his class was handing out invitations to his bday party, and another boy said "I'll be sure not to come" or something mean like that. My son said "Yes, I will come to your bday party" (luckily we can go, lol)! My son told me this story, and he knew the other boy made the bday boy sad. My son wanted him not to be sad, this was how he described the interaction. So he didn't just say yes for cake (though I'm sure that's a motivator)!
There are other examples, but that is one that sticks in my mind. So I would say he has empathy, but it's not consistent. Hopefully, it's evolving for him.