Link a Battle.net (and other game platforms) account to app with separated environments

Question

Actually, I have a web app with separated frontend (Angular 7) and backend (Symfony 4.2) environments. The users are connected with Google OAuth2. I would like to allow the users to link their game platforms account (like Battle.net, Steam, XBOX...) to their web app account (like Discord Connections). For this, I used Authorization Code Flow (https://develop.battle.net/documentation/guides/using-oauth/authorization-code-flow). I don't understand the workflow to achieve that, should I redirect the user from frontend directly to Auth page and redirect to API ? But if I do that, how can I retrieve the access token from the frontend part ?

Actually, the user click on a button from the frontend app, it redirect him to a backend route which build the oauth URL (with params like client_id, redirect_uri...) and then redirect to the authorization page.

After the user authentication on the Battle.net platform, it redirect the user to a backend callback with a code, but I don't know what to do with this, how to redirect or update the frontend after this action ?

Frontend :

<a href="{{ battleNetConnection }}" target="_blank" class="btn">Link your account</a>

<div class="container">
   <p *ngIf="!battleNet.account">You need to link your battle.net account first.</p>

   <!-- I need to update this part after the user have linked his account. -->
   <p *ngIf="battleNet.account">{{ battleNet.account.btag }}</p>
</div>

import { Component, OnInit } from '@angular/core';
import { environment } from '../../../../environments/environment';

@Component({
  selector: 'app-manage-platforms',
  templateUrl: './manage-platforms.component.html',
  styleUrls: ['./manage-platforms.component.scss']
})
export class ManagePlatformsComponent implements OnInit {
  public battleNetConnection = `${environment.api.url}/connections/battlenet`;

  constructor() {
  }

  ngOnInit() {}
}

Backend :

Controller :

class BattleNetController extends AbstractController
{
    /** @var BattleNetHttpClient $battleNetHttpClient */
    private $battleNetHttpClient;

    /**
     * @param BattleNetHttpClient $battleNetHttpClient
     */
    public function __construct(BattleNetHttpClient $battleNetHttpClient)
    {
        $this->battleNetHttpClient = $battleNetHttpClient;
    }

    /**
     * @Route("/connections/battlenet", name = "connections_battlenet")
     *
     * @return \Symfony\Component\HttpFoundation\RedirectResponse
     */
    public function authorize()
    {
        return $this->redirect($this->battleNetHttpClient->getAuthorizationUrl());
    }

    /**
     * @Route("/connections/battlenet/callback", name = "connections_battlenet_callback")
     *
     * @param Request $request
     */
    public function callback(Request $request)
    {
        $code = $request->get('code');
        // What am I supposed to do there ?
    }
}

Service :

class BattleNetHttpClient extends AbstractHttpClient
{
    const BASE_URI = 'https://eu.battle.net';
    const AUTH_ENDPOINT = '/oauth/authorize';

    /** @var array $config */
    private $config;

    /**
     * @param array        $config
     * @param HttpClient   $httpClient
     * @param RequestStack $requestStack
     */
    public function __construct(array $config, HttpClient $httpClient, RequestStack $requestStack)
    {
        parent::__construct($httpClient, $requestStack);
        $this->config = $config;
    }

    /** {@inheritdoc} */
    public function getAuthorizationUrl()
    {
        $params = http_build_query([
            'client_id'     => $this->config['client_id'],
            'redirect_uri'  => $this->getBaseUrl() . '/connections/battlenet/callback',
            'response_type' => 'code',
        ]);

        $url = self::BASE_URI . self::AUTH_ENDPOINT . '?' . $params;

        return $url;
    }
}

I would like to get user informations (like username, if he is actually logged in on this platform...) on the linked platform after the login, and then retrieve access_token from the platforms APIs to allow requests to them.