Make token budget context identity configurable (#36970)

## What changed

- Add a `features.token_budget.mode` setting with `thread` and `name` values.
- Default context-window metadata to the thread ID while allowing configurations to retain the agent name.
- Preserve the selected identity mode when applying model token-budget defaults and replaying locked configuration.

## Testing

- Cover configuration parsing and both identity formats in token-budget context messages.

GitOrigin-RevId: f6e6d2c49e09e70c0352e803bb65784ef77e5bee

codex-rs/core/src/session/mod.rs

@@ -3502,6 +3502,12 @@ impl Session {
                     session_source
                         .get_agent_path()
                         .unwrap_or_else(codex_protocol::AgentPath::root),
+                    turn_context
+                        .config
+                        .token_budget
+                        .as_ref()
+                        .map(|config| config.mode)
+                        .unwrap_or_default(),
                     auto_compact_window_ids.first_window_id,
                     auto_compact_window_ids.previous_window_id,
                     auto_compact_window_ids.window_id,