I found the fix, thanks to the Google translation of this Russian post. I want my JIDs to be simple TLDs like domainname.com. But the jabber configuration file /Library/Server/Messages/Config/jabberd/sm.xml specifies FQDNs that look like hostname.domainname.com. If you change this, Messages will work again -- apparently Server.app 2.2 has become more strict about this distinction. Do this:
sudo serveradmin stop jabber
sudo vi /Library/Server/Messages/Config/jabberd/sm.xml
<local> <!-- Who we identify ourselves as. Users will have this as the domain part of their JID. If you want your server to be accessible from other Jabber servers, this IDs must be FQDN resolvable by DNSes. If not set, the SM id is used. --> <id>domainname.com</id>
sudo serveradmin start jabber
Now Messages can authenticate to jabber using simple TLDs like firstname.lastname@example.org, just as before.