Check for $ _POST fields in a POST method form

I’m trying to check if the username and password fields are present in the login form.

The problem is that the if (!empty ($_POST)) code does not do this to me.

UPDATE:

if (isset($_POST['submit-btn'])) {

    //Sanitize POST Array
    $POST = filter_var_array($_POST, FILTER_SANITIZE_STRING);

    $username = $POST['username'];
    $password = $POST['password'];

    if(empty($username)) {
        echo "Username o email non inserita"; 
        return false;
    }

    if(empty($password)) {
        echo "Password non inserita"; 
        return false;
    }

    if($username && $password) {

        $login_array = array();
        $login_array['user_login'] = $username;
        $login_array['user_password'] = $password;

        $verify_user = wp_signon($login_array, true);
        if (!is_wp_error($verify_user)) {
            echo "<script>window.location = '" . site_url() . "'</script>";
        } else {
            echo 'Credenziali non valide!';
        }
    }
}

This is instead the login form that is on the same page, that is on the my-login.php page:

<form id="wp_login_form" action="/login/" method="post">
    <label class="my-username" >Username o Email</label>
    <input type="text" name="username" class="info-login" value="" placeholder="example@gmail.com">
    <label class="my-password" >Password</label>
    <input type="password" name="password" class="info-login" value="" placeholder="******">
    <label> 
    <input class="myremember" name="rememberme" type="checkbox" value="forever"><span class="hey">Remember me</span>
    </label> 
    <button type="submit" id="submitbtn" name="submit-btn" value="Login">Login</button>
</form>

Thanks a lot to those who will help me. Best regards.