Remove current category from post but display all others

First you need to get the categories of the current post, and then you can ‘exclude’ them by sending them through via the get_categories arguments array as $args['exclude'].

get_categories() uses get_terms(), you can see the list of available arguments you can use here.

We get the post terms with wp_get_post_terms() and make sure that we only get an array of ids and not an array of objects by passing it array("fields" => "ids") );

$args = array( 'parent' => 779 );

//Get the current post categories
$post_categories = wp_get_post_terms( get_the_ID(), 'category', array("fields" => "ids") );
if ( ! empty( $post_categories ) ) {
  //Here we make use of the exclude argument
  $args['exclude'] = $post_categories;
}

$categories = get_categories( $args );

Then you can just loop through your categories with your second snippet as you were earlier.

foreach ( $categories as $category ) {
    $value[] = array(
        'field_5cd186302ef1c' => $category->name,
    );
};
return $value;