Change the default template for category/tag search pages?

Hello,

I have a group project at school to make a website for a pretend archive. When opening a page which has generated a search for specific categories or tags, we’d like to add in a template part which shows the navigation and search terms like the one shown here : https://kapselminnen.org/archive and add it to the pages that appear when clicking on a category or tag link: https://kapselminnen.org/tag/double

The only way I can find to keep the categories/tags visible is to add them to the header, but then it is visible all the time and I’d prefer if it were only visible on specific pages related to post searches.

Thanks in advance!

The page I need help with: [log in to see the link]