[1 of 7] Add thread settings to UserInput (#23080)

**Stack position:** [1 of 7]

## Summary

The first three PRs in this stack are a cleanup pass before the actual
thread settings API work.

Today, core has several overlapping "user input" ops: `UserInput`,
`UserInputWithTurnContext`, and `UserTurn`. They differ mostly in how
much next-turn state they carry, which makes the later queued thread
settings update harder to reason about and review.

This PR starts that cleanup by adding the shared
`ThreadSettingsOverrides` payload and allowing `Op::UserInput` to carry
it. Existing variants remain in place here, so this layer is mostly a
behavior-preserving API shape change plus mechanical constructor
updates.

## End State After PR3

By the end of PR3, `Op::UserInput` is the only "user input" core op. It
can carry optional thread settings overrides for callers that need to
update stored defaults with a turn, while callers without updates use
empty settings. `Op::UserInputWithTurnContext` and `Op::UserTurn` are
deleted.

## End State After PR5

By the end of PR5, core will have only two ops for this area:

- `Op::UserInput` for user-input-bearing submissions.
- `Op::ThreadSettings` for settings-only updates.

## Stack

1. [1 of 7] [Add thread settings to
UserInput](https://github.com/openai/codex/pull/23080) (this PR)
2. [2 of 7] [Remove
UserInputWithTurnContext](https://github.com/openai/codex/pull/23081)
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/mcp-server/src/codex_tool_runner.rs

@@ -116,6 +116,7 @@ pub async fn run_codex_tool_session(
             }],
             final_output_json_schema: None,
             responsesapi_client_metadata: None,
+            thread_settings: Default::default(),
         },
         trace: None,
     };
@@ -165,6 +166,7 @@ pub async fn run_codex_tool_session_reply(
             }],
             final_output_json_schema: None,
             responsesapi_client_metadata: None,
+            thread_settings: Default::default(),
         })
         .await
     {