Configure PSP routing through the feature system (#38056)

## What changed

- Add the under-development `psp` feature and expose it in the config schema.
- Use the feature to attach the PSP cookie to first-party ChatGPT clients.
- Remove the hidden `--psp` flag and its process-scoped configuration plumbing.
- Preserve configured ChatGPT cookies when creating the PSP client used for GET and POST requests.

## Testing

- Update the config manager service test to verify that enabling `features.psp` retains the setting in the effective config and configures the expected ChatGPT cookie.

GitOrigin-RevId: 53acb5495d2ff71e4ed25f674a0cff787aea474a

codex-rs/app-server/src/in_process.rs

@@ -446,7 +446,7 @@ async fn start_uninitialized(args: InProcessStartArgs) -> IoResult<InProcessClie
         ));
 
         let processor_outgoing = Arc::clone(&outgoing_message_sender);
-        let mut config_manager = ConfigManager::new(
+        let config_manager = ConfigManager::new(
             args.config.codex_home.to_path_buf(),
             args.cli_overrides,
             args.loader_overrides,
@@ -455,7 +455,6 @@ async fn start_uninitialized(args: InProcessStartArgs) -> IoResult<InProcessClie
             args.arg0_paths.clone(),
             args.thread_config_loader,
         );
-        config_manager.psp = args.config.psp;
         let (processor_tx, mut processor_rx) = mpsc::channel::<ProcessorCommand>(channel_capacity);
         let mut processor_handle = tokio::spawn(async move {
             let processor = Arc::new(MessageProcessor::new(MessageProcessorArgs {