Count Codex background terminals

AGENTS.md

@@ -277,6 +277,11 @@ written, and the fold uses that same predicate to decide a reply is settled.
   subagent's own transcript; auto-resume can only schedule against a session.
   That is the case where the main agent is idle and a background Task is
   still burning quota.
+- **Codex's count is two id sets added together.** Open child thread ids come
+  from the subagent registry; live background command process ids come from
+  app-server's experimental `thread/backgroundTerminals/list`. The command set
+  is runtime state, refreshed at lifecycle edges and once a second while
+  nonempty. Never decrement it from an unmatched completion.
 - **The status word and its colour are `sessionStatusWord` /
   `sessionStatusColour`**, shared by the list and the session screen. They
   were two `when`s, and the second one silently missed `waiting`.