T.S.
My oldest one did not eat well at school because he was so excited and having fun being around new friends. He did that all year! So he got a snack when he got home or ate the rest of his lunch. I also tried to pack easy finger food hoping that would get him to eat more.
My second child did not like the noise and chaos of the first week of school. She cried about the whole lunchroom thing on the third day of school! And whined about it all week. It took her 2 weeks to settle into the routine and get used to all those people and all that noise. But she ate her food after just a few days.
My third child is more independent in that way so he just did his thing and ignored the chaos. But he also is sensitive to sound so he did complain about the noise.
If it were me I would go have lunch with her 'to meet her new friends and for fun'. But I would be scoping out how the kids are entering/exiting the room, bathroom breaks, etc. It is probably just that she is anxious and not sure what to do or how to do it. Some kids need a little more instruction than being herded into a room and told to eat. But I would keep it light and let her know that you care and want to know about her world while she is at school. That will go a long way in making her feel better, even if she still does not eat much.
OH, and some people don't like to eat in front of others. I never understood, but I have a friend like that. She will only eat a little bit and only certain things.
Good luck,