I am working a similar issue with some reddit users. No clear picture yet of how the Copilot button is being implemented, what Office/Outlook versions it shows up in, or any way to get rid of it.
Best anyone has found is to disable connected services. (As mentioned above). Sometime that makes it just a static icon. But it still doesn't go away.
https://www.reddit.com/r/Outlook/comments/1lem4c7/removing_copilot_dropdown_on_toolbar_outlook_2019/
Beyond that, all I can suggest is you punch the "I have this same problem" button and subscribe to this Answers Thread. Then wait for a miracle (Microsoft actually provides a fix).
Any brave soul out there who is having this problem who could do a ProcMon trace on Outlook startup and look for any possible clues? (Registry settings, DLL's loaded).
https://learn.microsoft.com/en-us/sysinternals/downloads/procmon
https://www.youtube.com/watch?v=ojUFjE00prA&t=14s
I can't do it, I don't have the Copilot button. My Outlook is too old.