Draft: Adjust ai-gateway no add on scenario to verify service access token

What does this MR do and why?

Now that code suggestions are available with Duo Core (i.e. no add on), we also need to wait for CloudConnector::SyncServiceTokenWorker to get the token necessary for accessing AI features. Prior to this change it would not wait so the test job was flaky.

https://gitlab.com/gitlab-org/gitlab/-/issues/547883#note_2557058254

Screenshots or screen recordings

The failures in https://gitlab.com/gitlab-org/gitlab-qa/-/pipelines/1865722731 seem unrelated

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

MR acceptance checklist

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