I don't have an exact solution to this unwanted prefix "EXTERNAL" in the From: field,
but I didn't know this was even happening until my colleague started railing about it... because my view does not show it.
FYI I have been using "Compact View" which apparently suppresses the display of this [External] feature,
path= Outlook365/ View/ ChangeView/ Compact .
When I select "Outlook365/ View/ ChangeView/ Single" then the "EXTERNAL" appears in From: .
MAYBE this will help others - I do not have any more notes on changing Outlook Views, but I expect there could be refinements. I agree this new feature is obtrusive, but it has not affected my work yet, and I do not normally see this feature.
May MS have mercy on our eyeballs