how to create blog post overview according to categories

I think it goes beyond the scope of Divi help. This is definitely JS with JQuery. It's using an event listener to display a lookup of a specific category. Maybe a search for a plugin that will do this that is Divi compatible?

 

It is simple enough to display a category menu and one category per page using a menu structure, but you will not remain on the same page when the button is clicked (you would go to the category page). With everything staying on the same page, you are defintely going to have to have some custom JS. If you are interested in a similar effect but going to each of the category pages, let me know and I can let you know how to proceed.

If it helps, it looks like the site you reference is using something called Raven or Raven Posts Classic. They are also using Elementor and not Divi. Unfortuntely. it looks like it is meant to be used with Elementor only.

 

I would create a new menu in Appearance >> Menus with the links to the categories. If you don't see categories under "Add menu items" you can turn it on under the screen options settings at the top of the page.

You can then add the menu to any Divi page - customize it as you see fit. If you like the button look, there will be some custom css, since the customizations in the Divi module are for the entire menu, not each element. Something like:

border: solid 1px #7b7b7b;
padding: 10px;
border-radius: 10px;

placed in the "Menu Link" custom css area of the Advanced tab.

I would use the Custom Theme Builder and add the menu to that, selecting "All Category Pages" for the assignment. This should choose all of the posts for the category of the page selected.

Under the menu section, You will want to include your content. Add a section with a blog module. Set "Posts For Current Page" to "Yes". In the Design Tab, set "Layout" to "Grid".

Let me know if it works!