[Waiting for user feedback] when a taxonomy is attached to a post in a non-default language, the taxonomy of the default langua...

{
    /** main post id*/
    $post_id;

    $trid = wpml_get_content_trid( 'post_docs', $post_id );
    $default_post_categories = wp_get_post_terms( $post_id, 'doc_category' );
    $languages = [ 'de', 'ru', 'uk' ];
    foreach ( $languages as $lang ) {
        $translated_post_id = wp_insert_post( [
            'post_title'   => 'title',
            'post_content' => 'content',
            'post_status'  => 'publish',
            'post_type'    => 'docs',
        ] );
        if ( ! is_wp_error( $translated_post_id ) ) {
            do_action( 'wpml_set_element_language', 'post_docs', $translated_post_id, $lang );
            do_action( 'wpml_set_element_language_details', [
                'element_id'    => $translated_post_id,
                'element_type'  => 'post_docs',
                'trid'          => $trid,
                'language_code' => $lang
            ] );
            if ( ! empty( $default_post_categories ) ) {
                foreach ( $default_post_categories as $term ) {
                    $object_id = apply_filters( 'wpml_object_id', $term->term_id, 'doc_category', false, $lang );
                    if ( $object_id ) {
                        wp_set_post_terms( $translated_post_id, [ $object_id ], 'doc_category' );
                    }
                }
            }
        }
    }
}

{
    //default lang in system is 'en'

    $default_lang_term_id = 48; //ID of the category of default language (language 'en')
    $default_lang_post_id = 4418; //Post ID of default language (post type 'post', language 'en')

    $translated_term_id = 85;  //ID of the of translated category (language 'de')
    $translated_post_id = 4568; //Post ID of translated post (post type 'post', language 'de')
    wp_set_post_terms( $translated_post_id, [ $translated_term_id ], 'category' );

    //in result: post with ID: 4568 has attached category with ID: 48 (expected ID: 85)
}