I recently updated to 22.04 and now I'm showing two WiFi icons. When I try and remove them with a right click like other icons I just get the WiFi network list. Is there a way to remove the one that is not part of the "Indicator Applet Complete"?
Hi mr.tapir , welcome to the community 
This might work:
gsettings set org.gnome.nm-applet show-applet false
You might need to logout and login again afterwards.
That didn't seem to have any effect, I rebooted after running it.
And thanks for the welcome!
You could , in your startup-entries, edit 'Network' and replace
nm-applet --indicator
to
nm-applet
Another way is to replace
indicator-applet-complete
with
indicator-applet