Derive collaboration settings from turn context (#32900)

## Why

`TurnContext` stored model and reasoning settings both as resolved turn fields and inside `CollaborationMode`, requiring the copies to stay synchronized when the model changed.

## What changed

- Store the mode and collaboration-mode developer instructions directly on `TurnContext`.
- Reconstruct `CollaborationMode` from those values plus the turn's current model and reasoning effort when callers need it.
- Read the mode directly for plan-mode checks, lifecycle events, and telemetry.

GitOrigin-RevId: b8fccafdd5d5cbccc84bc70d542588087ddf0093

codex-rs/core/src/context_manager/updates.rs

@@ -70,13 +70,11 @@ fn build_collaboration_mode_update_item(
     }
 
     let prev = previous?;
-    if prev.collaboration_mode.as_ref() != Some(&next.collaboration_mode) {
+    let collaboration_mode = next.collaboration_mode();
+    if prev.collaboration_mode.as_ref() != Some(&collaboration_mode) {
         // If the next mode has empty developer instructions, this returns None and we emit no
         // update, so prior collaboration instructions remain in the prompt history.
-        Some(
-            CollaborationModeInstructions::from_collaboration_mode(&next.collaboration_mode)?
-                .render(),
-        )
+        Some(CollaborationModeInstructions::from_collaboration_mode(&collaboration_mode)?.render())
     } else {
         None
     }