Delegate review to codex instance (#5572)

In this PR, I am exploring migrating task kind to an invocation of
Codex. The main reason would be getting rid off multiple
`ConversationHistory` state and streamlining our context/history
management.

This approach depends on opening a channel between the sub-codex and
codex. This channel is responsible for forwarding `interactive`
(`approvals`) and `non-interactive` events. The `task` is responsible
for handling those events.

This opens the door for implementing `codex as a tool`, replacing
`compact` and `review`, and potentially subagents.

One consideration is this code is very similar to `app-server` specially
in the approval part. If in the future we wanted an interactive
`sub-codex` we should consider using `codex-mcp`

codex-rs/core/src/state/turn.rs

@@ -37,16 +37,6 @@ pub(crate) enum TaskKind {
     Compact,
 }
 
-impl TaskKind {
-    pub(crate) fn header_value(self) -> &'static str {
-        match self {
-            TaskKind::Regular => "standard",
-            TaskKind::Review => "review",
-            TaskKind::Compact => "compact",
-        }
-    }
-}
-
 #[derive(Clone)]
 pub(crate) struct RunningTask {
     pub(crate) done: Arc<Notify>,
@@ -123,15 +113,3 @@ impl ActiveTurn {
         ts.clear_pending();
     }
 }
-
-#[cfg(test)]
-mod tests {
-    use super::TaskKind;
-
-    #[test]
-    fn header_value_matches_expected_labels() {
-        assert_eq!(TaskKind::Regular.header_value(), "standard");
-        assert_eq!(TaskKind::Review.header_value(), "review");
-        assert_eq!(TaskKind::Compact.header_value(), "compact");
-    }
-}