Feat: add isOther to question returned by request user input tool (#9890)

### Summary
Add `isOther` to question object from request_user_input tool input and
remove `other` option from the tool prompt to better handle tool input.

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

@@ -555,7 +555,7 @@ fn create_request_user_input_tool() -> ToolSpec {
 
     let options_schema = JsonSchema::Array {
         description: Some(
-            "Optional 2-3 mutually exclusive choices. Put the recommended option first and suffix its label with \"(Recommended)\". Only include \"Other\" option if we want to include a free form option. If the question is free form in nature, please do not have any option."
+            "Optional 2-3 mutually exclusive choices. Put the recommended option first and suffix its label with \"(Recommended)\". Do not include an \"Other\" option in this list; use isOther on the question to request a free form choice. If the question is free form in nature, please do not have any option."
                 .to_string(),
         ),
         items: Box::new(JsonSchema::Object {
@@ -586,6 +586,15 @@ fn create_request_user_input_tool() -> ToolSpec {
             description: Some("Single-sentence prompt shown to the user.".to_string()),
         },
     );
+    question_props.insert(
+        "isOther".to_string(),
+        JsonSchema::Boolean {
+            description: Some(
+                "True when this question should include a free-form \"Other\" option. Otherwise false."
+                    .to_string(),
+            ),
+        },
+    );
     question_props.insert("options".to_string(), options_schema);
 
     let questions_schema = JsonSchema::Array {
@@ -596,6 +605,7 @@ fn create_request_user_input_tool() -> ToolSpec {
                 "id".to_string(),
                 "header".to_string(),
                 "question".to_string(),
+                "isOther".to_string(),
             ]),
             additional_properties: Some(false.into()),
         }),

codex-rs/core/tests/suite/request_user_input.rs

@@ -94,6 +94,7 @@ async fn request_user_input_round_trip_resolves_pending() -> anyhow::Result<()>
             "id": "confirm_path",
             "header": "Confirm",
             "question": "Proceed with the plan?",
+            "isOther": false,
             "options": [{
                 "label": "Yes (Recommended)",
                 "description": "Continue the current plan."
@@ -213,6 +214,7 @@ where
             "id": "confirm_path",
             "header": "Confirm",
             "question": "Proceed with the plan?",
+            "isOther": false,
             "options": [{
                 "label": "Yes (Recommended)",
                 "description": "Continue the current plan."