Support waiting for code_mode sessions (#14295)

## Summary
- persist the code mode runner process in the session-scoped code mode
store
- switch the runner protocol from `init` to `start` with explicit
session ids
- handle runner-side session processing without the init waiter queue

## Validation
- just fmt
- cargo check -p codex-core
- node --check codex-rs/core/src/tools/code_mode_runner.cjs

codex-rs/core/src/codex.rs

@@ -1737,7 +1737,9 @@ impl Session {
                 config.features.enabled(Feature::RuntimeMetrics),
                 Self::build_model_client_beta_features_header(config.as_ref()),
             ),
-            code_mode_store: Default::default(),
+            code_mode_service: crate::tools::code_mode::CodeModeService::new(
+                config.js_repl_node_path.clone(),
+            ),
         };
         let js_repl = Arc::new(JsReplHandle::with_node_path(
             config.js_repl_node_path.clone(),