The old version of Google Sites had a commenting function built into it. Unfortunately, the current version of Google Sites doesn't have a commenting function built into it. There is a work-around that can work if you're sharing your Google Site with your colleagues and or students in the same G Suite for Education domain.
To create a news section that automatically updates in Google Sites and that your colleagues and or students can comment on, use a Google Document embedded into a page in your Google Site. To do this you'll create your Google Document then change its access permissions to allow anyone in your domain to comment on it. Then you'll embed the document into a page on your Google Site. Whenever you update the Google Document, the updated version will appear on your Google Site as well. In this short video I demonstrate the whole process of creating a dynamic news section in Google Sites.