All examples I found on internet refers to using inside , but nothing related to the use of e
Yes it is semantically correct to use header inside section
header – There is a crucial difference between the
headerelement and the general accepted usage ofheader(or masthead). There’s usually only oneheaderor ‘masthead’ in a page. In HTML5 you can have as many as you want. The spec defines it as “a group of introductory or navigational aids”. You can use aheaderin anysectionon your site. In fact, you probably should use aheaderwithin most of your sections. The spec describes thesectionelement as “a thematic grouping of content, typically with a heading.”
Source
You can also check header W3 specs here