Updated: September 2, 2020
This article has a somewhat cryptic title, because the problem I am going to show and resolve here is not trivial. Long story short, you installed the MATE desktop in Raspberry Pi OS. Things are working fine, except there's no network icon in the panel. The network WORKS, but you can't control it.
You may even have installed network-manager-gnome (Network Manager) and enabled it, but it shows as an empty icon, with no Wireless networks detected and listed. As it happens, I faced this problem when I setup my Raspberry Pi 4, and so, I'd like to show you how to fix this. The solution is not pretty, but it works. Let's get to it, to it, to it, to it ...
Problem in more detail & understand network setup
By default, Raspberry Pi OS comes with an LXDE desktop, and the Wireless network configuration is controlled via the WPA supplicant utility. This utility does not cooperate well with Network Manager if configured independently, which is why you're seeing the problems that you're seeing in MATE.
To resolve the problem we need to: a) disable WPA supplicant b) enable Network Manager.
WPA supplicant configuration resides under /etc/wpa_supplicant/wpa_supplicant.conf. Inside this file will be a list of your Wireless networks and their credentials. We want to "move" this configuration aside so that WPA supplicant does not establish a connection on next login.
sudo mv /etc/wpa_supplicant/wpa_supplicant /etc/wpa_supplicant/conf.bak
Next, install Network Manager:
sudo apt-get install network-manager-gnome
Enable it via Control Center > Startup Applications > checkbox network.
Verify Network Manager configuration - under /etc/NetworkManager/NetworkManager.conf. This is the default you get in MATE (for that matter, Ubuntu MATE):
That's it. Log out, log back in, and you should have Network Manager work and do its job properly:
Optional step: copy Ubuntu MATE configuration
As you may recall, I tested both Raspberry Pi OS and Ubuntu MATE on my Pi 4. If you're struggling with Network Manager, or something is off, simply copy the entire NetworkManager folder from /etc/ on the SD card with the Ubuntu MATE image to the SD card with the Raspberry Pi image!
Another hurdle unhurdled. If I may be permitted a super-corny joke, we're definitely in the HURD/Linux area rather than GNU/Linux area, hi hi ho ho. Now, on a more serious note, I am making fantastic progress with my Raspberry Pi 4, and being able to control network with a simple UI tool in MATE, or for that matter, Xfce or Plasma, opens a range of practical, useful possibilities. Without having this, Raspberry Pi OS had rather limited appeal to me.
Anyway, I hope you enjoyed this guide - we touched on some of the under-the-hood stuff, like WPA supplicant, Network Manager configuration, and if you're really in for the hack, you can even copy your settings from one SD card to another. I am now being inclined to try using other desktop environments - beyond what I've shown you already, that is, just to see how much fun I can have. Job done, see you around.