The feature is available only in Polylang Pro.
The ‘lang’ argument
It is possible to get posts or terms in only one language. For example:
1GET /wp/v2/posts?lang=fr
lists all posts in French, while
1GET /wp/v2/posts
lists all posts in all languages.
The ‘lang’ argument works for requests related to the posts and terms, whatever the post type or taxonomy.
The language and translations in responses
When querying posts or terms, two new fields are added to the response.
‘lang’: contains the language code (generally 2 letter ISO code) of the queried post or term.
‘translations’: contains an array with the language codes as keys and the id of the translated posts or terms as values. The array always includes the queried post or term itself.
Assign the language and translations
It is not only possible to get the language and translations of posts and terms but it is also possible to assign them. For example:
1POST /wp/v2/posts/3376?lang=fr&translations[en]=3374
will assign the French language to the post 3376 and link it to the post 3374 as its English translation. Note that you must first make sure that the post 3374 is in English.
Get the languages
Apart from extending the WP API, it is possible to get the languages with an additional endpoint:
1GET /pll/v1/languages
The response will include several properties such as:
name: native language name
slug: language code (generally 2 letter ISO code)
locale: WordPress locale
flag_url: the url of the flag associated to the language
home_url: the url of the home page in that language
page_on_front: if relevant, the id of the static front page in that language
page_for_posts: if relevant, the id of the page for posts in that language
The list above is not exhaustive as the response includes several other internal properties.