Using classic Outlook for Windows in business environments
I am on Win 10 with "Outlook for Microsoft 365 MSO (Version 2508 Build 16.0.19127.20192) 64-bit".
I had a poke around the Options and under Advanced > Outlook panes there's a check box labelled "Show Apps in Outlook". I unticked this, restarted Outlook and the offending CoPilot drop down was gone.
Now, I can't say the background "functionality" has been removed but I'm happier knowing that all I'm left with in that top right corner is the nag to switch to new Outlook (another enhancement no-one asked for).
Hope this helps!