This members-only tutorial provides the steps to automatically display posts in WordPress grouped by their categories.
We shall get all the non-empty categories in ascending order, loop through them, show the category title with the category archive link and for each, fetch three latest posts from that category, print the featured image + post title linked to the permalink for each post and style the output using CSS Grid.
While the steps are Oxygen-specific, this works in any WordPress site.
Step 1 - Register Custom Image Size
Register a custom image size for the featured images in the posts.