Chrome Extension - Getting CORS error when trying to fetch() from background script with manifest v3

I'm getting a CORS error when I try to do a request from my Chrome Extensions's background script. The background script is bundled with webpack.

Note: If I convert manifest.json to version 2 - all works fine. But with v3 it gives

Access to fetch at 'https://example.com/api/user/login' from origin 'chrome-extension://exampleid' has been blocked by CORS policy: No 'Access-Control-Allow-Origin' header is present on the requested resource. If an opaque response serves your needs, set the request's mode to 'no-cors' to fetch the resource with CORS disabled.

manifest.json

{
  "name": "__CE_APP_NAME__",
  "version": "__CE_APP_VERSION__",
  "manifest_version": 3,
  "background": {
    "service_worker": "background.bundle.js",
    "type": "module"
  },
  "content_scripts": [
    {
      "matches": [
        "https://example.com/*"
      ],
      "js": ["content.bundle.js"]
    }
  ],
  "web_accessible_resources": [
    {
      "resources": [ "images/*", "*.css" ],
      "matches": [
        "https://example.com/*"
      ]
    }
  ],
  "permissions": [
    "storage",
    "unlimitedStorage",
    "cookies",
    "identity"
  ],
  "host_permissions": [
    "<all_urls>"
  ]
}

background.js

chrome.runtime.onMessage.addListener((req) => {
  if (req.type === 'auth/login') {
    login(req.payload);
  }

  return true;
});

interface LoginCredentials {
  email: string;
  password: string;
}

const login = (data: LoginCredentials) => {
  fetch(`${API_BASE_URL}/user/login`, {
    method: 'POST',
    body: new URLSearchParams({
      email: data.email,
      password: data.password
    })
  })
    .then((response) => console.log(response))
    .catch((error) => console.log(error));
};