Extract request_user_input normalization into codex-tools (#16503)

## Why
This is another incremental step in the `codex-core` -> `codex-tools`
migration called out in `AGENTS.md`: keep pure tool-definition and
wire-shaping logic out of `codex-core` so the core crate can stay
focused on runtime orchestration.

`request_user_input` already had its spec and mode-availability helpers
in `codex-tools` after #16471. The remaining argument validation and
normalization still lived in the core runtime handler, which left that
tool split across the two crates.

## What Changed
- Export `REQUEST_USER_INPUT_TOOL_NAME` and
`normalize_request_user_input_args()` from
`codex-rs/tools/src/request_user_input_tool.rs`.
- Use that `codex-tools` surface from `codex-rs/core/src/tools/spec.rs`
and `codex-rs/core/src/tools/handlers/request_user_input.rs`.
- Keep the core handler responsible for payload parsing, session
dispatch, cancellation handling, and response serialization.

This is intended to be a straight refactor with no behavior change.

## Verification
- `cargo test -p codex-tools`
- `cargo test -p codex-core request_user_input`

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

@@ -7,6 +7,8 @@ use crate::tools::registry::ToolHandler;
 use crate::tools::registry::ToolKind;
 use async_trait::async_trait;
 use codex_protocol::request_user_input::RequestUserInputArgs;
+use codex_tools::REQUEST_USER_INPUT_TOOL_NAME;
+use codex_tools::normalize_request_user_input_args;
 use codex_tools::request_user_input_unavailable_message;
 
 pub struct RequestUserInputHandler {
@@ -33,9 +35,9 @@ impl ToolHandler for RequestUserInputHandler {
         let arguments = match payload {
             ToolPayload::Function { arguments } => arguments,
             _ => {
-                return Err(FunctionCallError::RespondToModel(
-                    "request_user_input handler received unsupported payload".to_string(),
-                ));
+                return Err(FunctionCallError::RespondToModel(format!(
+                    "{REQUEST_USER_INPUT_TOOL_NAME} handler received unsupported payload"
+                )));
             }
         };
 
@@ -46,31 +48,21 @@ impl ToolHandler for RequestUserInputHandler {
             return Err(FunctionCallError::RespondToModel(message));
         }
 
-        let mut args: RequestUserInputArgs = parse_arguments(&arguments)?;
-        let missing_options = args
-            .questions
-            .iter()
-            .any(|question| question.options.as_ref().is_none_or(Vec::is_empty));
-        if missing_options {
-            return Err(FunctionCallError::RespondToModel(
-                "request_user_input requires non-empty options for every question".to_string(),
-            ));
-        }
-        for question in &mut args.questions {
-            question.is_other = true;
-        }
+        let args: RequestUserInputArgs = parse_arguments(&arguments)?;
+        let args =
+            normalize_request_user_input_args(args).map_err(FunctionCallError::RespondToModel)?;
         let response = session
             .request_user_input(turn.as_ref(), call_id, args)
             .await
             .ok_or_else(|| {
-                FunctionCallError::RespondToModel(
-                    "request_user_input was cancelled before receiving a response".to_string(),
-                )
+                FunctionCallError::RespondToModel(format!(
+                    "{REQUEST_USER_INPUT_TOOL_NAME} was cancelled before receiving a response"
+                ))
             })?;
 
         let content = serde_json::to_string(&response).map_err(|err| {
             FunctionCallError::Fatal(format!(
-                "failed to serialize request_user_input response: {err}"
+                "failed to serialize {REQUEST_USER_INPUT_TOOL_NAME} response: {err}"
             ))
         })?;
 

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

@@ -15,6 +15,7 @@ use codex_protocol::openai_models::ApplyPatchToolType;
 use codex_protocol::openai_models::ConfigShellToolType;
 use codex_tools::CommandToolOptions;
 use codex_tools::DiscoverableTool;
+use codex_tools::REQUEST_USER_INPUT_TOOL_NAME;
 use codex_tools::ShellToolOptions;
 use codex_tools::SpawnAgentToolOptions;
 use codex_tools::TOOL_SEARCH_DEFAULT_LIMIT;
@@ -344,7 +345,7 @@ pub(crate) fn build_specs_with_discoverable_tools(
             /*supports_parallel_tool_calls*/ false,
             config.code_mode_enabled,
         );
-        builder.register_handler("request_user_input", request_user_input_handler);
+        builder.register_handler(REQUEST_USER_INPUT_TOOL_NAME, request_user_input_handler);
     }
 
     if config.request_permissions_tool_enabled {