Add experimental context management activation (#42385)

## What changed

- Add the under-development `features.context_management.experimental_mode` configuration and schema.
- For eligible ChatGPT Plus, Pro, and Pro Lite sessions using the Codex backend, enable token-budget context, history notes, and the `new_context` tool when experimental context management is configured.
- Keep the feature disabled for custom providers, provider credentials, non-Codex endpoints, and temporary structured threads.

## Testing

- Cover subscription eligibility, backend restrictions, configuration resolution, token-budget guidance, and temporary-thread overrides.

GitOrigin-RevId: 19402af19c4d69e09a7cdb3687ee7d233f6a562a

codex-rs/tui/src/app/tests/recap_generation_tests.rs

@@ -407,7 +407,7 @@ async fn temporary_recap_threads_disable_memories_and_remote_mcp_servers() -> Re
     let codex_home = tempdir()?;
     std::fs::write(
         codex_home.path().join("config.toml"),
-        "[mcp_servers.filesystem]\ncommand = 'true'\n",
+        "features.context_management.experimental_mode = true\n[mcp_servers.filesystem]\ncommand = 'true'\n",
     )?;
     app.config.codex_home = codex_home.path().to_path_buf().abs();
     app.config.sqlite = codex_state::SqliteConfig::new_for_testing(codex_home.path().abs());
@@ -433,6 +433,7 @@ async fn temporary_recap_threads_disable_memories_and_remote_mcp_servers() -> Re
     let starts = recorded_params(&requests, "thread/start");
     assert_eq!(starts.len(), 1);
     assert_eq!(starts[0]["config"]["features.memories"], false);
+    assert_eq!(starts[0]["config"]["features.context_management"], false);
     assert!(starts[0]["config"].get("features.memory_tool").is_none());
     assert_eq!(
         starts[0]["config"]["mcp_servers"]["filesystem"]["enabled"],

codex-rs/tui/src/temporary_structured_request.rs

@@ -60,6 +60,7 @@ pub(crate) async fn start_temporary_thread(
         ("features.apps".to_string(), false.into()),
         ("features.code_mode".to_string(), false.into()),
         ("features.code_mode_only".to_string(), false.into()),
+        ("features.context_management".to_string(), false.into()),
         ("features.current_time_reminder".to_string(), false.into()),
         ("features.deferred_executor".to_string(), false.into()),
         ("features.enable_fanout".to_string(), false.into()),