Header styles are different from heading styles which are different from table styles. You would normally never use a heading style in a header.

Heading styles in Word have a lot of special qualities that make them unsuited for use in a header and very suited for use in the body of a document. Why use Microsoft Word’s built-in heading styles? by Shauna Kelly

Understanding Styles in Microsoft Word

All formatting in a template should be done using Styles.

I never use table styles so I will not pretend to know much about them.