How to see the SQL Queries being executed in WordPress REST API

You can add the following filter and you will see the queries in the Response Header.

// Define a global variable to store SQL queries
global $wp_rest_api_queries;
$wp_rest_api_queries = array();

// Hook to capture SQL queries
add_filter('query', 'capture_rest_api_queries');

function capture_rest_api_queries($query) {
    global $wp_rest_api_queries;

    // Only capture queries made during REST API requests
    if (defined('REST_REQUEST') && REST_REQUEST) {
        $wp_rest_api_queries[] = $query;
    }

    return $query;
}

// Hook to add captured SQL queries to REST API response headers
add_filter('rest_post_dispatch', 'add_sql_queries_to_header', 10, 3);

function add_sql_queries_to_header($response, $server, $request) {
    global $wp_rest_api_queries;

    // Add SQL queries to response headers
    $response->header('X-SQL-Queries', json_encode($wp_rest_api_queries));

    return $response;
}