Getting the underlying OAuth Http Client for usage with e.g. Google Calendar Api

I am currently having difficulties using the already authenticated OAuth user and making calls to other APIs like the Google Calendar API to e.g. get the calendar entries. I have successfully authenticated the user using OAuth2 doing the following:

Client client = Client()
      .setEndpoint('url')
      .setProject('id');
Account account = Account(client);
await account.createOAuth2Session(
      provider: OAuthProvider.google,
      success: "http://localhost:8080/auth/oauth2/success",
      failure: "http://localhost:8080/auth/oauth2/failure",
      scopes: ['openid', 'https://www.googleapis.com/auth/calendar'],
    );

I now have access to the current user and the session:

loggedInUser = await account.get();
currentSession = await account.getSession(sessionId: 'current');

I now want to use this authenticated OAuth client to make requests (and also handle refresh tokens) to other APIs. The Google Calendar API for example takes a modified http client that sends the Authorization header with every request. For example:

var googleCalendar = CalendarApi(<http.Client>);
calendarList = await googleCalendar.calendarList.list();

My question is: How can I get the already authorized httpClient from the Appwrite SDK so that i can use it to call other SDKs and also make common REST API calls using the http client itself? I see that the Client object has a method call() which uses the internal httpClient to do exactly what I describe (Using the underlying httpClient to make authorized requests). I am currently doing the following as a workaround and it gets pretty messy handling the refresh and scopes for both flutter libraries (Using the OAuth Flutter Package: https://pub.dev/packages/oauth2):

currentOAuth2Client = oauth2.Client(
  oauth2.Credentials(
    currentSession.providerAccessToken,
    ...
  ),
);