I am trying to make query_vars work in rest api. In my code bellow if I call wp-json/wp/v2/cpt?city=test, my debug output always returns an empty string.

<?php
/**
 * Plugin Name: Test
 * Author:      Gecka <contact@gecka.nc>
 * License:     GNU General Public License v3 or later
 * License URI: http://www.gnu.org/licenses/gpl-3.0.html
 */

function cpt_init() {
    $args = [
        'label'               => 'Custom post',
        'supports'            => [ 'title', 'revisions', 'custom-fields' ],
        'show_in_rest'        => true,
        'hierachical'         => false,
        'public'              => true,
        'exclude_from_search' => true,
        'show_ui'             => true,
    ];
    register_post_type( 'cpt', $args );
}
add_action( 'init', 'cpt_init' );

function cpt_register_query_vars( $vars ) {
    $vars[] = 'city';
    return $vars;
}
add_filter( 'query_vars', 'cpt_register_query_vars' );

function cpt_posts_where( $where, WP_Query $wp_query ) {
    if('cpt' !== $wp_query->get('post_type') ) {
        return $where;
    }

    // debug output
    var_export( $wp_query->get('city') );
    
    return $where;
}
add_filter( 'posts_where', 'cpt_posts_where', null, 2 );