Finish moving codex exec to app-server (#15424)

This PR completes the conversion of non-interactive `codex exec` to use
app server rather than directly using core events and methods.

### Summary
- move `codex-exec` off exec-owned `AuthManager` and `ThreadManager`
state
- route exec bootstrap, resume, and auth refresh through existing
app-server paths
- replace legacy `codex/event/*` decoding in exec with typed app-server
notification handling
- update human and JSONL exec output adapters to translate existing
app-server notifications only
- clean up "app server client" layer by eliminating support for legacy
notifications; this is no longer needed
- remove exposure of `authManager` and `threadManager` from "app server
client" layer

### Testing
- `exec` has pretty extensive unit and integration tests already, and
these all pass
- In addition, I asked Codex to put together a comprehensive manual set
of tests to cover all of the `codex exec` functionality (including
command-line options), and it successfully generated and ran these tests

codex-rs/app-server/src/outgoing_message.rs

@@ -527,38 +527,6 @@ impl OutgoingMessageSender {
         }
     }
 
-    pub(crate) async fn send_notification_to_connections(
-        &self,
-        connection_ids: &[ConnectionId],
-        notification: OutgoingNotification,
-    ) {
-        let outgoing_message = OutgoingMessage::Notification(notification);
-        if connection_ids.is_empty() {
-            if let Err(err) = self
-                .sender
-                .send(OutgoingEnvelope::Broadcast {
-                    message: outgoing_message,
-                })
-                .await
-            {
-                warn!("failed to send notification to client: {err:?}");
-            }
-            return;
-        }
-        for connection_id in connection_ids {
-            if let Err(err) = self
-                .sender
-                .send(OutgoingEnvelope::ToConnection {
-                    connection_id: *connection_id,
-                    message: outgoing_message.clone(),
-                })
-                .await
-            {
-                warn!("failed to send notification to client: {err:?}");
-            }
-        }
-    }
-
     pub(crate) async fn send_error(
         &self,
         request_id: ConnectionRequestId,
@@ -616,7 +584,6 @@ impl OutgoingMessageSender {
 #[serde(untagged)]
 pub(crate) enum OutgoingMessage {
     Request(ServerRequest),
-    Notification(OutgoingNotification),
     /// AppServerNotification is specific to the case where this is run as an
     /// "app server" as opposed to an MCP server.
     AppServerNotification(ServerNotification),
@@ -624,13 +591,6 @@ pub(crate) enum OutgoingMessage {
     Error(OutgoingError),
 }
 
-#[derive(Debug, Clone, PartialEq, Serialize)]
-pub(crate) struct OutgoingNotification {
-    pub method: String,
-    #[serde(default, skip_serializing_if = "Option::is_none")]
-    pub params: Option<serde_json::Value>,
-}
-
 #[derive(Debug, Clone, PartialEq, Serialize)]
 pub(crate) struct OutgoingResponse {
     pub id: RequestId,