Show pod items on “lastest posts” page

You’re running into the famous issue of WP hard coding all their widgets and archives to only work for “post” post-types. If you want your other post types to be included in all archives, you have to include that post-type in the pre_get_posts filter.

Is mostly depends on what you’re using for latest posts: https://wordpress.stackexchange.com/questions/241060/display-custom-post-type-in-recent-posts

If you’re using a widget, you can use Custom Post Types Widgets plugin to get your custom Post Types included.