Did you ask her... why she is not eating?
Maybe, the other kids are too distracting?
And, Kindergarten kids... do not have a sense of timing nor time... and that they may only have 20 minutes to eat.
Thus, they come home, having not eaten.
Try talking to her Teacher.
Because yes, the goal as you said is she just eat something and at home is where you feed her balanced.
The main thing is she is not getting hypoglycemic, due to lack of intake ALL day. Hence coming home after school, all tired/fussy/very cranky.
7-8 hours without food since breakfast, will do that to even an adult.
My son is in Kinder. He is a picky eater. BUT... he has been, eating the school lunches. At school. Our public school has good lunches. Not icky food. Other than that, previously at Preschool, he had home lunch. The SAME type of sandwich everyday. That way, he ate.
Oh, when you pick your child up after school, ALREADY have at least something in the car for her to eat. Because, by then, she is in hypoglycemic levels. Having not eaten all day. So, even if you give her a 1/2 cup of grapes or some nuts... at least that will help her blood sugar levels from being depleted.
That is what I do. I have something IN the car already, for my kids when I pick them up from school.
Ask your child. Find something that she will eat. Then, make that even if it is everyday.
Explain to her... that it is important for her BODY... that she eat... otherwise, her body will run out of energy and then she can't concentrate or focus or feel good at school. That food, is a body's fuel.
I explain that, to my son who is 5. I tell him, eat his lunch FIRST... that is important. THEN you can talk and chat. And if another kid is distracting you... tell the cafeteria Aid or tell the child "Can you stop bothering me, I have to eat."