Show Codex background task counts

SUBAGENTS.md

@@ -169,7 +169,11 @@ until that activity edge. The root's `turn/completed` reports `waiting` while
 the registry contains an open child, and the last activity completion reports
 `idle` if the root is between turns. Because the child thread id is also the
 on-disk id, an adopted driver can route and finish a child whose spawn record
-is already behind the durable stdout offset.
+is already behind the durable stdout offset. The registry's open count is also
+Codex's `backgroundTasks` measurement: lifecycle changes send it through the
+same event and session-summary fields as Claude's provider snapshot. Codex
+background commands are not counted because app-server supplies no complete
+set of them.
 
 A subagent that was mid-flight when the backend restarted keeps working:
 the registry reopens the existing transcript on the next child line, and