Filterig for post_format?

WordPress’ WP Query supports this through the post_format arg, but this is not marked as a public query argument. You can add the following to your site’s code to enable it as a public query argument, but keep in mind that it may cause privacy concerns:

add_filter( 'json_query_vars', function ( $vars ) {
    $vars[] = 'post_format';
    return $vars;
} );