This is an accepted solution.
Welcome to Shopify Community.
Aibek is here from Speedimize.io
We would have thrown off the ready-made code, but then we will need to change the structure of header.liquid and style it.
Move the topbar down under the logo, but at the same time put the basket icon on the same level as the logo. If you display the trash icon, the styles will not be applied, since it depends on the parent class. Here you already need to add styles and rewrite existing ones.
The easiest option is to hire a developer. The task is easy, it will take a maximum of 1 hour. You can hire on Fiverr or Shopify experts.
Hope that suits you.