Hi there, recently got my own Fairphone 5 and also found the NFC icon annoying.
While the UI tuner linked earlier wasn’t able to remove it, I found this one was able to do so:
It does require a bit of adb tweaking, so presumably this isn’t supported by Fairphone and may stop working in a future update, but I figured I’d share my findings here for the people stumbling upon this thread from searches.