Improve Default mode prompt (less confusion with Plan mode) (#10545)

## Summary

This PR updates `request_user_input` behavior and Default-mode guidance
to match current collaboration-mode semantics and reduce model
confusion.

## Why

- `request_user_input` should be explicitly documented as **Plan-only**.
- Tool description and runtime availability checks should be driven by
the **same centralized mode policy**.
- Default mode prompt needed stronger execution guidance and explicit
instruction that `request_user_input` is unavailable.
- Error messages should report the **actual mode name** (not aliases
that can read as misleading).

## What changed

- Centralized `request_user_input` mode policy in `core` handler logic:
  - Added a single allowed-modes config (`Plan` only).
  - Reused that policy for:
    - runtime rejection messaging
    - tool description text
- Updated tool description to include availability constraint:
  - `"This tool is only available in Plan mode."`
- Updated runtime rejection behavior:
  - `Default` -> `"request_user_input is unavailable in Default mode"`
  - `Execute` -> `"request_user_input is unavailable in Execute mode"`
- `PairProgramming` -> `"request_user_input is unavailable in Pair
Programming mode"`
- Strengthened Default collaboration prompt:
  - Added explicit execution-first behavior
  - Added assumptions-first guidance
  - Added explicit `request_user_input` unavailability instruction
  - Added concise progress-reporting expectations
- Simplified formatting implementation:
  - Inlined allowed-mode name collection into `format_allowed_modes()`
- Kept `format_allowed_modes()` output for 3+ modes as CSV style
(`modes: a,b,c`)

codex-rs/core/src/tools/spec.rs

@@ -9,6 +9,7 @@ use crate::tools::handlers::apply_patch::create_apply_patch_json_tool;
 use crate::tools::handlers::collab::DEFAULT_WAIT_TIMEOUT_MS;
 use crate::tools::handlers::collab::MAX_WAIT_TIMEOUT_MS;
 use crate::tools::handlers::collab::MIN_WAIT_TIMEOUT_MS;
+use crate::tools::handlers::request_user_input_tool_description;
 use crate::tools::registry::ToolRegistryBuilder;
 use codex_protocol::config_types::WebSearchMode;
 use codex_protocol::dynamic_tools::DynamicToolSpec;
@@ -623,9 +624,7 @@ fn create_request_user_input_tool() -> ToolSpec {
 
     ToolSpec::Function(ResponsesApiTool {
         name: "request_user_input".to_string(),
-        description:
-            "Request user input for one to three short questions and wait for the response."
-                .to_string(),
+        description: request_user_input_tool_description(),
         strict: false,
         parameters: JsonSchema::Object {
             properties,