fix(conversation_store,admin,cli): keep session when file lags db, sort pty by recency

src/beaver_gateway/agents/claude.py

@@ -171,6 +171,16 @@ class ClaudeCodeOptions(BaseModel):
     terminal assistant has been seen. Bound on extra latency when
     ``wait_for_turn_duration=True``."""
 
+    idle_session_ttl: float = 1800.0
+    """Seconds a pooled claude session may sit unused before it is
+    terminated. The backend pools live PTYs by conversation-history
+    fingerprint; when a conversation forks, the session behind the old
+    fingerprint becomes unreachable but stays resident — one live
+    ``claude`` (hundreds of MB) each. 30 minutes keeps an active chat
+    warm across a coffee break while bounding what a fork storm can
+    strand. There is no count cap: concurrent conversations should all
+    stay warm. ``0`` disables reaping."""
+
 
 class ClaudeAgent(BaseAgent):
     """Agent backed by ``claude-code-api``.