You have instantiated $episodes outside of your loop right?
If I understand you correctly, you have an array of arrays now in $episodes and you want it to be one array of values instead? So kind of like flattening the array? It might help if you explain why you want to do this. But perhaps something like this:
$episodes = [];
while( $animes->have_posts() ) {
$animes->the_post();
$args = array(
'orderby' => 'meta_value_num',
'order' => 'DESC',
'fields' => 'all',
'meta_query' => [['key' => 'episode_number','type' => 'NUMERIC',]]
);
$episodes[$i] = wp_get_post_terms(intval( $post->ID ), 'episodes', $args );
}
function flatten(array $array) {
$return = array();
array_walk_recursive($array, function($a) use (&$return) { $return[] = $a; });
return $return;
}
$flattened_episodes = flatten($episodes);
var_dump($flattened_episodes);
See How to Flatten a Multidimensional Array? for more on flattening an array. Docs here on the array_walk_recursive function - https://php.net/array_walk_recursive