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/app-server/src/bespoke_event_handling.rs

@@ -278,6 +278,7 @@ pub(crate) async fn apply_bespoke_event_handling(
                         id: question.id,
                         header: question.header,
                         question: question.question,
+                        is_other: question.is_other,
                         options: question.options.map(|options| {
                             options
                                 .into_iter()

codex-rs/app-server/tests/common/responses.rs

@@ -67,6 +67,7 @@ pub fn create_request_user_input_sse_response(call_id: &str) -> anyhow::Result<S
             "id": "confirm_path",
             "header": "Confirm",
             "question": "Proceed with the plan?",
+            "isOther": false,
             "options": [{
                 "label": "Yes (Recommended)",
                 "description": "Continue the current plan."