WP Rest API - Retrieve sub page by full slug (URL/Path)

file.php

<?php 

if (strstr($slug, '/')) {
    $segments = explode('/', $slug);
    $parent_id = null;

    foreach ($segments as $key => $segment) {
        $params['slug'] = $segment;

        if ($parent_id) {
            $params['parent'] = $parent_id;
        }

        $page = $this->client->pages()->get(null, $params);

        if (empty($page)) {
            return [];
        }

        $parent_id = $page->id;
    }

    return $page;
} else {
    $func = $this->client->pages();

    if ($id) {
        return $func->get($id);
    } else {
        return $func->get(null, ['slug' => $slug]);
    }
}

I've crafted a few different solutions as an answer to this WPSE question. It was a really interesting problem to explore :)