Icon over thumbnail according to post format

You can use get_post_format($post_id) to retrieve each post’s format, then you can assign a class to each post based on it’s format.

Once you have that, you only need to define said classes to, for example, show an icon overlay on the ::after pseudo-element of the posts.

To obtain consistency between widgets, category pages, etc. you can either apply the previous to each or use a unified post template for everything.