For interoperability, we should have well-known names for statuses. Haze doesn't use the well-known names for extended-away and hidden, which means Empathy's fairly simplistic status selector can't set them; Haze's names are also not in Mission Control's list of fallbacks. Pseudo-patch:

 static const TpPresenceStatusSpec statuses[] = {
     { "available", TP_CONNECTION_PRESENCE_TYPE_AVAILABLE, TRUE,
         arg_specs, NULL, NULL },
     { "busy", TP_CONNECTION_PRESENCE_TYPE_BUSY, TRUE,
         arg_specs, NULL, NULL },
     { "away", TP_CONNECTION_PRESENCE_TYPE_AWAY, TRUE,
         arg_specs, NULL, NULL },
-    { "ext_away", TP_CONNECTION_PRESENCE_TYPE_EXTENDED_AWAY, TRUE,
-        arg_specs, NULL, NULL },
+    { "xa", TP_CONNECTION_PRESENCE_TYPE_EXTENDED_AWAY, TRUE,
+        arg_specs, NULL, NULL },
-    { "invisible", TP_CONNECTION_PRESENCE_TYPE_HIDDEN, TRUE, NULL, NULL, NULL },
+    { "hidden", TP_CONNECTION_PRESENCE_TYPE_HIDDEN, TRUE, NULL, NULL, NULL },
     { "offline", TP_CONNECTION_PRESENCE_TYPE_OFFLINE, FALSE, NULL, NULL, NULL },
     { NULL, TP_CONNECTION_PRESENCE_TYPE_UNSET, FALSE, NULL, NULL, NULL }
 };