Cleanup collaboration mode variants (#10404)

## Summary

This PR simplifies collaboration modes to the visible set `default |
plan`, while preserving backward compatibility for older partners that
may still send legacy mode
names.

Specifically:
- Renames the old Code behavior to **Default**.
- Keeps **Plan** as-is.
- Removes **Custom** mode behavior (fallbacks now resolve to Default).
- Keeps `PairProgramming` and `Execute` internally for compatibility
plumbing, while removing them from schema/API and UI visibility.
- Adds legacy input aliasing so older clients can still send old mode
names.

## What Changed

1. Mode enum and compatibility
- `ModeKind` now uses `Plan` + `Default` as active/public modes.
- `ModeKind::Default` deserialization accepts legacy values:
  - `code`
  - `pair_programming`
  - `execute`
  - `custom`
- `PairProgramming` and `Execute` variants remain in code but are hidden
from protocol/schema generation.
- `Custom` variant is removed; previous custom fallbacks now map to
`Default`.

2. Collaboration presets and templates
- Built-in presets now return only:
  - `Plan`
  - `Default`
- Template rename:
  - `core/templates/collaboration_mode/code.md` -> `default.md`
- `execute.md` and `pair_programming.md` remain on disk but are not
surfaced in visible preset lists.

3. TUI updates
- Updated user-facing naming and prompts from “Code” to “Default”.
- Updated mode-cycle and indicator behavior to reflect only visible
`Plan` and `Default`.
- Updated corresponding tests and snapshots.

4. request_user_input behavior
- `request_user_input` remains allowed only in `Plan` mode.
- Rejection messaging now consistently treats non-plan modes as
`Default`.

5. Schemas
- Regenerated config and app-server schemas.
- Public schema types now advertise mode values as:
  - `plan`
  - `default`

## Backward Compatibility Notes

- Incoming legacy mode names (`code`, `pair_programming`, `execute`,
`custom`) are accepted and coerced to `default`.
- Outgoing/public schema surfaces intentionally expose only `plan |
default`.
- This allows tolerant ingestion of older partner payloads while
standardizing new integrations on the reduced mode set.

## Codex author
`codex fork 019c1fae-693b-7840-b16e-9ad38ea0bd00`

codex-rs/app-server/tests/suite/v2/collaboration_mode_list.rs

@@ -1,8 +1,8 @@
 //! Validates that the collaboration mode list endpoint returns the expected default presets.
 //!
 //! The test drives the app server through the MCP harness and asserts that the list response
-//! includes the plan, coding, pair programming, and execute modes with their default model and reasoning
-//! effort settings, which keeps the API contract visible in one place.
+//! includes the plan and default modes with their default model and reasoning effort
+//! settings, which keeps the API contract visible in one place.
 
 #![allow(clippy::unwrap_used)]
 
@@ -45,23 +45,8 @@ async fn list_collaboration_modes_returns_presets() -> Result<()> {
     let CollaborationModeListResponse { data: items } =
         to_response::<CollaborationModeListResponse>(response)?;
 
-    let expected = [
-        plan_preset(),
-        code_preset(),
-        pair_programming_preset(),
-        execute_preset(),
-    ];
-    assert_eq!(expected.len(), items.len());
-    for (expected_mask, actual_mask) in expected.iter().zip(items.iter()) {
-        assert_eq!(expected_mask.name, actual_mask.name);
-        assert_eq!(expected_mask.mode, actual_mask.mode);
-        assert_eq!(expected_mask.model, actual_mask.model);
-        assert_eq!(expected_mask.reasoning_effort, actual_mask.reasoning_effort);
-        assert_eq!(
-            expected_mask.developer_instructions,
-            actual_mask.developer_instructions
-        );
-    }
+    let expected = vec![plan_preset(), default_preset()];
+    assert_eq!(expected, items);
     Ok(())
 }
 
@@ -77,35 +62,11 @@ fn plan_preset() -> CollaborationModeMask {
         .unwrap()
 }
 
-/// Builds the pair programming preset that the list response is expected to return.
-///
-/// The helper keeps the expected model and reasoning defaults co-located with the test
-/// so that mismatches point directly at the API contract being exercised.
-fn pair_programming_preset() -> CollaborationModeMask {
+/// Builds the default preset that the list response is expected to return.
+fn default_preset() -> CollaborationModeMask {
     let presets = test_builtin_collaboration_mode_presets();
     presets
         .into_iter()
-        .find(|p| p.mode == Some(ModeKind::PairProgramming))
-        .unwrap()
-}
-
-/// Builds the code preset that the list response is expected to return.
-fn code_preset() -> CollaborationModeMask {
-    let presets = test_builtin_collaboration_mode_presets();
-    presets
-        .into_iter()
-        .find(|p| p.mode == Some(ModeKind::Code))
-        .unwrap()
-}
-
-/// Builds the execute preset that the list response is expected to return.
-///
-/// The execute preset uses a different reasoning effort to capture the higher-effort
-/// execution contract the server currently exposes.
-fn execute_preset() -> CollaborationModeMask {
-    let presets = test_builtin_collaboration_mode_presets();
-    presets
-        .into_iter()
-        .find(|p| p.mode == Some(ModeKind::Execute))
+        .find(|p| p.mode == Some(ModeKind::Default))
         .unwrap()
 }

codex-rs/app-server/tests/suite/v2/turn_start.rs

@@ -365,7 +365,7 @@ async fn turn_start_accepts_collaboration_mode_override_v2() -> Result<()> {
     let ThreadStartResponse { thread, .. } = to_response::<ThreadStartResponse>(thread_resp)?;
 
     let collaboration_mode = CollaborationMode {
-        mode: ModeKind::Custom,
+        mode: ModeKind::Default,
         settings: Settings {
             model: "mock-model-collab".to_string(),
             reasoning_effort: Some(ReasoningEffort::High),