Header search was a custom implemeted and we implemented error validation for it.
For News one we tried to make it work however it's coming from facets and inside facets, auto search is not required. It can be submitted without any characters or with typed characters.
We can write down to facetwp about this issue.
We can not display error validation for an empty search as we already spent like 10-15 hours to make it work however it seems impossible to make it an error validation message for an empty search.