Hi there,
you can use the Block Element, which comes in a few varieties:
1. Block Element – Content Template:
https://docs.generatepress.com/article/block-element-content-template/
With this you can use the GenerateBlocks plugin to design the post card, to replace the archives content template.
And this can be applied to any archive page including Search Results
2. Block Element – Page Hero:
https://docs.generatepress.com/article/block-element-page-hero/
Essentially a Block Element HooK:
https://docs.generatepress.com/article/block-element-hook/
The page hero is the same as the hook but has some pre-configurations for you so it appears in the Hero section. And removes stuff ( like title and featured images ) in place of the hero section.
So with the Hook type you can insert content into the various template hooks that you can see the main ones here:
https://docs.generatepress.com/article/hooks-visual-guide/
With those options, you can redesign the archives post card, and insert other content before or after the list of posts.