I don’t think you mean a literal feed as in RSS. Feed display depends upon your feed reader, not WP. WP simply sends out feed data, it’s not formatted. I think instead you mean a “category archive list”. You’re forgiven for using the wrong terminology ??
You’ll need a customized theme template to accomplish what you want. A blog archive list normally uses the index.php template. It’s also possibly used for other kinds of requests, so it is not a good candidate for customizing. If this kind of category archive is intended to be the site’s home page, I suggest in reading settings having the site display a “static” page as home. It won’t actually be static though, it’s just what the setting calls it. Before doing this, create a WP page for the purpose. You only need a title, nothing else is needed, but you could add some content if you like. You also should have another empty page for a traditional blog archive list, even if you don’t intend to use it, relying on a custom home page template instead.
Start with an existing theme template such as page.php or index.php. Copy it into a new file named front-page.php. This lets your custom template pick up the usual theme styling such as header and footer. If you added any content to the page, the existing loop on the template will display it. There is likely other output on the template you may want to remove, such as the page’s title and page meta data. You might not want a sidebar either, if there is one to start with. Same for comments.
On this template you will make 4 separate queries by instantiating WP_Query objects. Use one of the category parameters to limit the posts queried. For each query, the linked doc page has some basic loop examples you can use to output the query results. Include whatever HTML you need to break up the page into 4 sections.
The actual column or grid layout is achieved with CSS. The additional CSS could be within a <style> block that’s output by the template since it will only apply to this one page. Any added CSS that should be applied site-wide should go in the Additional CSS section of the customizer.
These suggestions are for a classic, PHP template based theme. If you use a block theme instead, the general concept is the same, but the way templates are used will be different since block theme templates are plain .html files, no PHP is on block theme templates. PHP in block themes is managed as patterns instead.
