Fix native integration to pass cookies/credentials for "Extensions" info graphql request

Created by: erzhtor

Closes https://github.com/sourcegraph/sourcegraph/issues/32599.

Description

This PR:

• Fixes native integration (aka @sourcegraph/code-host-integration) not passing cookies/credentials when fetching Extensions info via GraphQL API.

Test plan

1. Check browser extension works correctly/as previsously
2. Check native integration works correctly
   1. Build native integration npm package locally: yarn --cwd client/browser build
   2. Setup GitLab locally using gdk
   3. Link a local npm package to gitlab:
      1. cd client/browser/build/integration && yarn link
      2. `cd to /gitlab && yarn link @sourcegraph/code-host-integration)
   4. Restart GitLab gdk restart
   5. Run sourcegraph locally and configure native integration w/ local GitLab`
   6. Open any synced w/ local Sourcegraph repository in local GitLab and check hovers work as expected and no errors in DevTools/Network tab

Screenshots

Before	After

Before merging

• Test on different code hosts (if applicable)

  • GitHub
  • Gitlab
  • GitHub Enterprise
  • Refined GitHub
  • Phabricator
  • Phabricator integration
  • Bitbucket
  • Bitbucket integration

• Test on different browsers (if applicable)

  • Chrome
  • Firefox
  • Safari

• Add change log message to client/browser/CHANGELOG.md, under "Unreleased" section. (if applicable)

App preview:

• Link