Hello,
According to your description, I reproduced your scenario in follow steps:
I created a custom business required field in Case entity and added this column to the header of case form. Then created a new case and filled the required field in other sections except header and clicked save, the record was saved.
Only if you move your mouse cursor to focus on the business required input field, the “Required fields must be filled in” message pops up. This may be a feature of by-design.

As a suggestion, you can move the business required field to other section except header, or you can add the same business required field to other section.