Why does is_user_logged_in() return false after redirect from another site?

I am developing a WordPress site that redirects to an external payment gateway after a user registers for the site. After the user makes a payment the user is redirected to a page to complete their sign up.

Edit for clarification:
Here is the code used for the redirect:

  //code ran after a user signs up located in functions.php

  function process_user(){
    $first_name = $params[1]["first"];
    $last_name = $params[1]["last"];
    $email = $params[3]["value"];
    $password = $params[11]["value"];
    $user_args = array(
      "user_login" => $email,
      "user_pass" => $password,
      "user_email" => $email,
      "first_name" => $first_name,
      "last_name" => $last_name,
      "role" => "subscriber"
    );
    // add user
    wp_insert_user($user_args);
    $user = get_user_by('email',$email);

    //log out user if logged in
    if(is_user_logged_in()){
      wp_logout();
      wp_set_current_user(0);
    }
    $login_data = array();
    $login_data['user_login'] = $email;
    $login_data['user_password'] = $password;
    $login_data['remember'] = true;
    $user = wp_signon($login_data);
    if(!is_wp_error($user)){
        wp_set_current_user( $user->ID, $email );
        wp_set_auth_cookie( $user->ID, true, false );
        wp_redirect("https://another_payment_gateway.com");
        exit;
    }
  }

 add_action( 'wpforms_process_complete_1011','process_user',10, 3 );

The user is redirected and fills out the payment form. Upon success the user is redirected to a landing page. If they are not logged in they are shown a dialog for non logged in users. The landing page contains a shortcode function that is also located in functions.php

Here is the shortcode function:

//shortcode function from functions.php

add_shortcode( 'user_signup_completion', function(){
  ob_start();
  include(get_stylesheet_directory().'/user_signup_completion.php');
  $contents = ob_get_contents(); // put the buffer into a variable
  ob_end_clean();
  return $contents;
});

   //excerpt from user_signup_completion.php
    if(is_user_logged_in()){
      $user = wp_get_current_user();
      //code for logged in users
    }else{
      //message for non logged in users 
    }

The shortcode is used on a page created by a user in WordPress. I hope that this further explain what is going on.

If I go to the account page it is shown that the user is logged in. But when redirected from a different site is_user_logged_in() returns false.
Any insight into this issue would be much appreciated.

Where are you triggering the second code block (that includes is_user_logged_in())? That code may be triggered before set_current_user, which is called after plugins_loaded.

I would take a look at the action reference and see if you are calling your check before WordPress is aware of the user.