Firebase REST API 401 unauthorized for everyone but me

Question

I'm using firebase's real time database to store data, and I have permission rules set to:

{
  "rules": {
    "users": {
      "$uid": {
        ".write": "$uid === auth.uid",
        ".read": "$uid === auth.uid"
      }
    }
  }
}

I'm trying to read and write to the database using rest/fetch, and it seems to be working fine. But after some investigation, it seems it only works for me specifically, and other users receive a 401 unauthorized response. My code looks like

chrome.identity.getAuthToken({ interactive: true }, (token) => {
    let url = this.url + `users/${id}.json?access_token=${token}`;
    const headers = new Headers({
      "Content-Type": "application/json",
    });

    fetch(url, { headers: headers })
      .then((res) => {
        console.log(res);
        return res.json();
      })
  });

Token is obtained by calling getAuthToken from the extensions background page. id is found by calling chrome.identity.getProfileUserInfo:

chrome.identity.getProfileUserInfo((info) => {
      email = info.email;
      userId = info.id;
    });

I also have the following scope, which I thought would enable reading and writing from firebase: https://www.googleapis.com/auth/datastore

Any ideas? I'm very confused why it would work, but only for me.