Google App script Wepp App for logged users only

I have been searching stack overflow for a solution but none worked yet and I am not really sure if I can do what I want to, but here is the scenario:

I have a Google app script that will return only this:

function doPost(e) {
  return ContentService.createTextOutput(JSON.stringify({status: "success", "data": "my-data"})).setMimeType(ContentService.MimeType.JSON);
}
function doGet(e) {
  return ContentService.createTextOutput(JSON.stringify({status: "success", "data": "my-data"})).setMimeType(ContentService.MimeType.JSON);
}

I have an app deployed with the current configurations:
Execute as: Me, Who has access: Anyone with Google Account

I am buinding a Javascript script that will run on the browser scope and call that app, however I want to have an oAuth and get an access token before calling it. However either I cannot find a solution or it doesn’t exist with only front-end solutions.

I tried using Javascript fetch, however I either get unauthorized responses or ‘opaque’ responses, I already figured out that one of the configurations of the fetch should be {redirect: ‘follow’}, because app script always redirects to a new URL.

I might not be able to use Google Cloud Platform internally for this purpose, that is why I didn’t go through the API deployment path.

I do not have a backend, this script will run either injected through a bookmark or if we get approval through a chrome extension, so it is browser scopped;