More strangeness - i connected to irc.c0la.se, and then disconnected, and it still had the full network name. But then I remembered that I had added the network to my servers.ini, and the servers.ini group description of the current server seems to govern the disconnected $network value. So i deleted the the-c0la-network entry from servers.ini, and suddenly i get:
*** disconnected 23-net
.. which was the previous network I had been at. I deleted the servers.ini entry for 23-net, and then $network shows the network description name of the network that shows in the connect window after 23-net got deleted.