How to authenticate through Google Cloud IAP with client from gapi (google-api-javascript-client) library?

Question

Given a client-side app (written in Angular, but it's not much important) where I use google-api-javascript-client library to authenticate users. In a way described here - https://developers.google.com/sheets/api/quickstart/js:

      gapi.load('client:auth2', () => {
        gapi.client.init({
          clientId: CLIENT_ID,
          scope: SCOPES,
          discoveryDocs: DISCOVERY_DOCS
        }).then(() => {
          gapi.auth2.getAuthInstance().isSignedIn.listen(this.onSigninStatusChanged.bind(this));
          const isSignedIn = gapi.auth2.getAuthInstance().isSignedIn.get();
          if (!isSignedIn) {
            gapi.auth2.getAuthInstance().signIn({prompt: 'select_account'});
          }
        });
      });

Now I want to access a backend in AppEngine behind Identity-Aware Proxy (IAP).

I tried naively to pass a token from GoogleUser via http request's authorization header, but it doesn't seem to work (getting 401):

    let token = gapi.auth2.getAuthInstance().currentUser.get().getAuthResponse().id_token;
    this.http.get<Config>('https://myservice-dot-myproject.ew.r.appspot.com/api/get',
      {
        headers: { 'Authorization': 'Bearer ' + token}
      });

I guess I need somehow to use OAuth Client ID from IAP. I found a sample on how to do it with nodejs auth client. But can't find a way to do it with the client-side google-api-javascript-client lib.

UPDATE: I found a nice online resource to verify token that I got from GoogleUser.getAuthResponse().id_token - https://oauth2.googleapis.com/tokeninfo?id_token=token (source), it display the following:

{
  "iss": "accounts.google.com",
  "azp": "my OAuth Client ID that I used in gapi (CLIENT_ID)",
  "aud": "OAuth Client ID that I used in gapi (CLIENT_ID)",
  "sub": "user id (number)",
  "hd": "Google user GSuite domain",
  "email": "Google user email",
  "email_verified": "true",
  "at_hash": "some hash",
  "name": "Google user name",
  "picture": "an url",
  "given_name": "Google user firstname",
  "family_name": "Google user lastname
  "locale": "en",
  "iat": "1615972232",
  "exp": "1615975832",
  "jti": "87129b6c0f684b0bc7beac9df5e522e6272c13f1",
  "alg": "RS256",
  "kid": "6a8ba5652a7044121d4fedac8f14d14c54e4895b",
  "typ": "JWT"
}