“… none of the offered feeds [RSS does – mine] seem to include information on the language of the content….”
“It is because Frédéric, polylang’s author has not set his taxonomy property ‘show_in_rest’ => true …”
“The plugin author is not planning to add this to the free version. The pro version will get something that could provide for this…”
function wpse_modify_taxonomy() {
// get the arguments of the already-registered taxonomy
$language_args = get_taxonomy( 'language' ); // returns an object
// make changes to the args
// in this example there are three changes
// again, note that it's an object
$language_args->show_in_rest = true;
// re-register the taxonomy
register_taxonomy( 'language', 'post', (array) $language_args );
}
// hook it up to 11 so that it overrides the original register_taxonomy function
add_action( 'init', 'wpse_modify_taxonomy', 11 );
It could be slow, it could be something else, but it works.
Source: How to know the language of a post through the WordPress REST API | WordPress.org