Route message-board notifications through agent mailboxes (#59139)

## Why

Board notifications were skipped when recipients had no active turn accepting mailbox delivery. Queue them through the ordinary agent-message path so idle recipients can receive them in a later turn.

## What changed

- Submit board notices as `Op::InterAgentCommunication` with `trigger_turn` disabled, preserving normal mailbox scheduling without reopening finalized answers.
- Hold a residency guard through dispatch of submitted agent messages to coordinate delivery with agent eviction.
- Update board tool descriptions to describe the host's notification queueing and wake policy.

## Testing

Update local and HTTP board scenarios to cover queued idle notices, delivery after a finalized answer, and mailbox delivery before a pending tool call. Extend residency coverage to verify that submission waits for the eviction gate and queued messages survive eviction.

GitOrigin-RevId: a77137fc40932f5903852e14742483844e07c9bc

codex-rs/core/src/session/input_queue.rs

@@ -7,7 +7,6 @@ use codex_diagnostics::GaugeGuard;
 use codex_history::ResponseItemEnvelope;
 use codex_protocol::ThreadId;
 use codex_protocol::models::ResponseItem;
-use codex_protocol::protocol::InterAgentCommunication;
 use codex_protocol::turn_input::TurnStartOptions;
 use codex_protocol::user_input::UserInput;
 use serde::Deserialize;
@@ -202,38 +201,6 @@ impl InputQueue {
         (activity_rx, pending_activity)
     }
 
-    #[expect(
-        clippy::await_holding_invalid_type,
-        reason = "active turn checks and turn state updates must remain atomic"
-    )]
-    pub(crate) async fn deliver_mailbox_communication_to_current_turn(
-        &self,
-        active_turn: &Mutex<Option<ActiveTurn>>,
-        communication: InterAgentCommunication,
-        expected_turn_id: Option<&str>,
-    ) -> bool {
-        let active = active_turn.lock().await;
-        let Some(active_turn) = active.as_ref().filter(|turn| {
-            turn.task.as_ref().is_some_and(|task| {
-                expected_turn_id.is_none_or(|id| {
-                    task.turn_context.sub_id == id && !task.cancellation_token.is_cancelled()
-                })
-            })
-        }) else {
-            return false;
-        };
-        let mut turn_state = active_turn.turn_state.lock().await;
-        if !turn_state.accepts_mailbox_delivery_for_current_turn() {
-            return false;
-        }
-        turn_state
-            .pending_input
-            .items
-            .push(TurnInput::InterAgentCommunication(communication.into()));
-        self.activity_tx.send_replace(InputQueueActivity::Mailbox);
-        true
-    }
-
     pub(crate) async fn enqueue_mailbox_communication(
         &self,
         communication: crate::PendingAgentMessage,
@@ -556,6 +523,7 @@ mod tests {
     use super::*;
     use codex_history::CodexHarnessMetadata;
     use codex_protocol::AgentPath;
+    use codex_protocol::protocol::InterAgentCommunication;
     use codex_protocol::user_input::UserInput;
     use pretty_assertions::assert_eq;