Reconcile Claude background task state

SUBAGENTS.md

@@ -86,6 +86,20 @@ transcript is still being written to and its process is the session's to stop.
    status ends it from the update, since the failure to avoid is a subagent
    nothing ever finishes.
 
+   Since Claude Code 2.1.261, `background_tasks_changed { tasks: [...] }` is
+   the authoritative level beside those edges: its set replaces the previous
+   set, so a missed terminal edge cannot leave a subagent running forever. Its
+   ids are deliberately not correlated with the edge stream; the useful claim
+   here is whether the set is empty. The edges still carry mapping, outcome
+   and closing summary. On adoption the driver sends a repeated `initialize`,
+   which makes a current CLI send the full set; an older CLI accepts it and sends no level,
+   leaving the edge-based path unchanged. A snapshot is reconciled immediately
+   when the persisted parent status proves it is between turns, and otherwise
+   at the next `result` boundary -- while a turn is open, a foreground agent is
+   legitimately absent from the background set. Reconciliation writes
+   `Status Exited`, which is also what makes a formerly stale row deletable;
+   a task notification ordered after the level can still add its summary.
+
    The two rules this replaces were both wrong, in opposite directions. The
    parent's `tool_result` is not it: a backgrounded Task's arrives at launch
    ("Async agent launched..."), so ending there truncated a running agent's
@@ -117,12 +131,12 @@ transcript is still being written to and its process is the session's to stop.
 
    **While any task is outstanding the session's turn ends in
    `Status Waiting` rather than `Idle`.** `Idle` means "waiting for a person",
-   and a session with a backgrounded subagent is not doing that. Two sources:
-   the translator's `open_tasks`, and `Subagents::any_open` -- which is what
-   covers a subagent launched before a backend restart adopted the session,
-   whose `task_started` is behind the offset its stdout is read from. That
-   second lookup is also what lets such a subagent's ending be recognised at
-   all.
+   and a session with a backgrounded subagent is not doing that. The edge
+   fallback has two sources: the translator's `open_tasks`, and
+   `Subagents::any_open` -- which covers a subagent launched before a backend
+   restart adopted the session, whose `task_started` is behind the durable
+   stdout offset. On current Claude versions the replace-semantics level above
+   reconciles both at a safe turn boundary.
 
    **A limit the account hits inside a subagent is hoisted to the session**
    as well as recorded here, because `resume.rs` can only schedule against a