Let’s save a few hundred words 🙂
I would like to achieve this as my hero section on a static homepage of a new website: https://mymodernmet.com/
Technically they show the latest post from the blog.
The full width background image is the post featured image and the post category, title, excerpt and read more link (styled as a button) are displayed in the white overlay located in the right half of the hero section.
It will definitely take some custom CSS to style them.
As for using the featured image as background image, you just need to turn on the background image in page header without uploading one then it will automatically grab the featured image for each post for you.