Remove legacy collaboration mode variants (#36990)

## What changed

- Remove the hidden `PairProgramming` and `Execute` variants from `ModeKind`.
- Delete their unused prompt templates and simplify mode handling to cover only `Default` and `Plan`.

GitOrigin-RevId: 8d24e3f562a09e3071b2decae275d2b3871a1e9c

codex-rs/core/src/context/world_state/collaboration_mode.rs

@@ -26,7 +26,6 @@ impl CollaborationModeState {
             catalog_messages.and_then(|messages| match collaboration_mode.mode {
                 ModeKind::Default => messages.default.as_ref(),
                 ModeKind::Plan => messages.plan.as_ref(),
-                ModeKind::PairProgramming | ModeKind::Execute => None,
             });
 
         Self {

codex-rs/core/src/tools/handlers/request_user_input_spec_tests.rs

@@ -171,17 +171,6 @@ fn request_user_input_unavailable_messages_respect_default_mode_feature_flag() {
         ),
         None
     );
-    assert_eq!(
-        request_user_input_unavailable_message(ModeKind::Execute, &default_available_modes()),
-        Some("request_user_input is unavailable in Execute mode".to_string())
-    );
-    assert_eq!(
-        request_user_input_unavailable_message(
-            ModeKind::PairProgramming,
-            &default_available_modes()
-        ),
-        Some("request_user_input is unavailable in Pair Programming mode".to_string())
-    );
 }
 
 #[test]