It should look like this, with a slightly different theme:
That’s actually a frontend for NetworkManager (manpage). (settings found in /etc/NetworkManager)
Per the manual “NetworkManager does not manage any interface defined in /etc/network/interfaces by default”
I have checked both my Ubuntu machine and my L4t machine and the files are both there. Settings should be saved, but I’ve noticed it has some bugs, such as this one I just had where settings won’t apply. It should be saving settings. If it isn’t, that sounds like a bug in either NetworkManager or gnome-control-center.
Again, I would recommend just managing /etc/network/interfaces as these things tend not to happen as often. It could be the complete lack of any /etc/network/interfaces is part of the problem. If those files are missing, other things in /etc/ might be as well. I will reflash my nano with a stock image later and test. In the mean time you could try “nmtui” or “nmcli” (alternative NetworkManager frontends) to see if they work. If they don’t, then the problem is very like NetworkManager related. If they do, it’s more likely the gnome-control-center network panel.