[2 of 7] Remove UserInputWithTurnContext (#23081)

**Stack position:** [2 of 7]

## Summary

This PR removes the overlapping `Op::UserInputWithTurnContext` variant
now that `Op::UserInput` can carry thread settings overrides directly.

## Stack

1. [1 of 7] [Add thread settings to
UserInput](https://github.com/openai/codex/pull/23080)
2. [2 of 7] [Remove
UserInputWithTurnContext](https://github.com/openai/codex/pull/23081)
(this PR)
3. [3 of 7] [Remove
UserTurn](https://github.com/openai/codex/pull/23075)
4. [4 of 7] [Placeholder for OverrideTurnContext
cleanup](https://github.com/openai/codex/pull/23087)
5. [5 of 7] [Replace OverrideTurnContext with
ThreadSettings](https://github.com/openai/codex/pull/22508)
6. [6 of 7] [Add app-server thread settings
API](https://github.com/openai/codex/pull/22509)
7. [7 of 7] [Sync TUI thread
settings](https://github.com/openai/codex/pull/22510)

codex-rs/app-server/src/request_processors/turn_processor.rs

@@ -502,37 +502,31 @@ impl TurnRequestProcessor {
                 })?;
         }
 
+        let thread_settings = codex_protocol::protocol::ThreadSettingsOverrides {
+            cwd,
+            workspace_roots: runtime_workspace_roots,
+            profile_workspace_roots,
+            approval_policy,
+            approvals_reviewer,
+            sandbox_policy,
+            permission_profile,
+            active_permission_profile,
+            windows_sandbox_level: None,
+            model,
+            effort,
+            summary,
+            service_tier,
+            collaboration_mode,
+            personality,
+        };
+
         // Start the turn by submitting the user input. Return its submission id as turn_id.
-        let turn_op = if has_any_overrides {
-            Op::UserInputWithTurnContext {
-                items: mapped_items,
-                environments: environment_selections,
-                final_output_json_schema: params.output_schema,
-                responsesapi_client_metadata: params.responsesapi_client_metadata,
-                cwd,
-                workspace_roots: runtime_workspace_roots,
-                profile_workspace_roots,
-                approval_policy,
-                approvals_reviewer,
-                sandbox_policy,
-                permission_profile,
-                active_permission_profile,
-                windows_sandbox_level: None,
-                model,
-                effort,
-                summary,
-                service_tier,
-                collaboration_mode,
-                personality,
-            }
-        } else {
-            Op::UserInput {
-                items: mapped_items,
-                environments: environment_selections,
-                final_output_json_schema: params.output_schema,
-                responsesapi_client_metadata: params.responsesapi_client_metadata,
-                thread_settings: Default::default(),
-            }
+        let turn_op = Op::UserInput {
+            items: mapped_items,
+            environments: environment_selections,
+            final_output_json_schema: params.output_schema,
+            responsesapi_client_metadata: params.responsesapi_client_metadata,
+            thread_settings,
         };
         let turn_id = self
             .submit_core_op(&request_id, thread.as_ref(), turn_op)