Term: Fix header to fit design

The header looks weird when we have a site logo:

<img width="1417" alt="Screenshot 2024-06-18 at 17 12 26" src="https://github.com/WordPress/community-themes/assets/3593343/892737dc-cf10-49ad-8f05-b66ee1ea2da8">

Let's fix the alignment and tweak the header so it looks more like [figma](https://www.figma.com/community/file/1263420783737936752)