Separation of responsibilities between infrastructure and services (business) layers

Question

In application user should be able to authorize using his twitch account, here is how business requirements looks like:

1. for twitch authorization user should be redirected (by the backend application) to the twitch authentication page
2. after logging in on twitch side:
   _ if user was not found in our application - new user should be created and then logged in to our application
   _ if user already existed - it should be logged in
3. then user should be redirected back to the frontend application

And here is how I've managed to do it:

// this class represents business logic
class TwitchAuthService {
  // this method returns url and then controller redirects user to the appropriate page
  public getRedirectionUrlToStartAuth = (
    { successUrl, failUrl }: { successUrl: string; failUrl: string; }
  ): string => {
    return 'https://id.twitch.tv/oauth2/authorize?' +
      new URLSearchParams({
        response_type: 'code',
        client_id: this.twitchId,
        redirect_uri: this.getRedirectUrl(),
        scope: 'user:read:email',
        state: `successUrl=${successUrl}&failUrl=${failUrl}`,
      })
  }
  
  // after receiving token from twitch, we 
  // - return already existing user or
  // - create a new one and return it
  authenticateUser() { ... }
}

And at the moment when I receive callback from twitch, I have to parse successUrl and failUrl parameters from twitch-url in response for further redirection (I've provided these parameters earlier while using getRedirectionUrlToStartAuth method)

I've created a separate method for this "parsing" functionality, getRedirectUrlsFromCallback but where should I locate it?

Is it still part of business logic? Or should I create some infrastructure service for Twitch and put this method here? Or it simply can be added as private method of the controller?

  public getRedirectUrlsFromCallback = (state: string): { successUrl: string; failUrl: string } => {
    const urlParams = new URLSearchParams(state);
    const successUrl = urlParams.get('successUrl');
    const failUrl = urlParams.get('failUrl');

    if (!successUrl || !failUrl) {
      throw new IncorrectCallbackUrlError();
    }

    return {
      successUrl,
      failUrl,
    }
  }