How to get taxonomies in another language using wpblobus?

Question

API

Good afternoon.
On the page I display taxonomies in the sidebar and posts.
I filter using vue.

Created 2 api for taxonomies

function cats_register_search()
{
    register_rest_route('cats/v1', 'search', [
        'methods' => WP_REST_SERVER::READABLE,
        'callback' => 'catsResults',
    ]);
}

add_action('rest_api_init', 'cats_register_search');
function catsResults()
{
    $terms = get_terms([
        'taxonomy' => 'cat',
        'hide_empty' => true,
    ]);

    return $terms;
}

And posts

function portfolio_register_search()
{
    register_rest_route('portfolio/v1', 'search', [
        'methods' => WP_REST_SERVER::READABLE,
        'callback' => 'portfolioSearchResults',
    ]);
}

add_action('rest_api_init', 'portfolio_register_search');
function portfolioSearchResults($data)
{
    $portfolio_result = [];

    if ($data['term'] === "all") {
        $portfolio = new WP_Query([
            'post_type' => 'portfolio',
            'posts_per_page' => -1
        ]);
    } else {
        $portfolio = new WP_Query([
            'post_type' => 'portfolio',
            'posts_per_page' => -1,
            'tax_query' => array(
                array(
                    'taxonomy' => 'cat',
                    'field' => 'slug',
                    'terms' => $data['term']
                )
            )
        ]);
    }

    while ($portfolio->have_posts()) {
        $portfolio->the_post();
        $id = get_the_ID();
        $term = get_the_terms($id, 'cat')[0];
        $term_name = $term->name;
        $url = get_field('single_portfolio')['link'];
        $parent_term = get_term($term->parent, 'cat');

        array_push($portfolio_result, [
            'title' => get_the_title(),
            'img' => get_the_post_thumbnail_url(get_the_ID(), 'full'),
            'term_name' => $term_name,
            'url' => $url,
            'parent_term' => $parent_term
        ]);
    }
    return $portfolio_result;
}

And on the page I filter posts by taxonomies.

const appFilter = new Vue({
        el: "#search",
        data: {
            home_url: '',
            filtered: [],
            cat_search: 'all',
            cats: [],
            cats_parent: [],
            cats_child: [],
            cats_filtered: [],
            loading: true
        },
        methods: {
            filterProducts(term) {
                this.loading = true;
                this.cat_search = term;
                fetch(this.home_url + '/wp-json/portfolio/v1/search?term=' + this.cat_search)
                    .then(response => response.json())
                    .then(res => {
                        this.filtered = res;
                        console.log(this.filtered, 'this.filtered')
                        setTimeout(() => {
                            this.loading = false;
                        }, 200);
                    })
                    .catch(error => console.log(error, 'error'))
            }
        },
        mounted() {
            this.home_url = window.location.origin;
            fetch(this.home_url + '/wp-json/cats/v1/search')
                .then(response => response.json())
                .then(res => {
                    this.cats = res;
                    if (Object.prototype.toString.call(this.cats) !== '[object Array]') {
                        this.cats = Object.values(this.cats);
                    }
                    this.cats_parent = this.cats.filter(item => item.parent === 0);
                    this.cats_child = this.cats.filter(item => item.parent !== 0);
                    this.cats_filtered = this.cats_parent.map(item => {
                        return {
                            parent: {
                                "name": item.name,
                                "slug": item.slug
                            },
                            children: this.cats_child.filter(child => child.parent === item.term_id)
                        };
                    });
                    this.filterProducts('all')
                })
                .catch(error => console.log(error, 'error'))
        }
    });

The task has changed, now you need to add several languages.
The problem is that get_terms on the worpdress page are automatically translated when changing the language, but how do I do it in the file where I create the api.
I understand that I can set the parameter / en, / ru, but how to get taxonomies and posts with translation?

Thanks in advance.