WP API Authentication can not set the cookie - wordpress

Question

i try to make API authentication with my WP app
i have write the add the below code to add new fields and upon login it send data to External API if it user exist in API return login or create new WP user if not just don't do anything or gives an error, but i have the issue with Cookie now and get the "Error: Cookies are blocked due to unexpected output."
here is my code:
add_action('login_form', 'businessId', 10, 1);
function businessId()
{
?>
<div class="businessid_wrap">
<label for="businessId">business ID</label>
<input type="text" id="businessId" name="businessId" value=""/>
</div>
<?php
}
function au_auth($user, $username, $password)
{
$endpoint = 'will be my API endpoint url';
// Makes sure there is an endpoint set as well as username and password
if (!$endpoint || $user !== null || (empty($username) && empty($password))) {
return false;
}
$auth_args = [
'method' => 'POST',
'headers' => [
'Content-type: application/json',
],
'sslverify' => false,
'body' => [
'businessId' => $_POST['businessId'],
'userLogin' => $username,
'userPassword' => $password,
],
];
$response = wp_remote_post($endpoint, $auth_args);
$body = json_decode($response['body'], true);
var_dump ($response);
if (!$response) {
// User does not exist, send back an error message
$user = new WP_Error('denied', __('<strong>Error</strong>: Your username or password are incorrect.'));
} elseif ($response) {
/for now i just dumping the return data to check
var_dump ($response);
}
remove_action('authenticate', 'wp_authenticate_username_password', 20);
return $user;
}
add_filter('authenticate', 'au_auth', 10, 3);