How to display title and featured image only when category is chosen

The file you are looking for is content.php.

You can find more informations about Template hierarchy here: https://developer.wordpress.org/themes/basics/template-hierarchy/

The sections you have to get rid of are the divs:

<div class="entry-content">
...
...
</div>

<div class="entry-footer">
...
...
</div>

So you have many ways to achieve it, the simpler is to clone the file in your child theme, then wrap these divs in an IF statement like the example below, in order to check if the current page is a category or not:

if( !is_category() ):

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