OK, so I figured this out. The problem was that after upgrading, the file /etc/dovecot/notify.plist contained just the “notification_server_enabled” key, and none of the rest.
As a result, the push_notify daemon had opened the socket, but was blocking inside the XMPP code waiting to connect to the Jabber server, and was therefore not servicing the UNIX socket it uses to talk to dovecot.
The solution in the end was to stop and start everything, and turn push notifications off and on again, until servermgrd rewrote the file to contain the necessary server details.