You’re indirectly answering your question yourself:
The notification channel, as I mentioned, supports SMTP and sendmail.
It however does not support XOAUTH for Google or Microsoft 365.
The documentation also states this.
So a send connector just for your Zammad instance that doesn’t require authentication (make sure to only allow it for your Zammad host…) could be the solution.
Other solutions might be feasable as well, but depend on your environment and what you can technically do. Most people decide for providers like Microsoft or Google for reasons, be it functionality or “it just working” (most of the times).