Add process-scoped PSP routing for ChatGPT requests (#36986)

## What changed

- Add a hidden global `--psp` runtime flag and propagate it through TUI, exec,
  app-server, remote-control, and in-process startup paths.
- Attach the `oai-chat-psp=true` cookie to first-party ChatGPT requests when
  enabled, using a cached cookie-aware client with sensitive request logging
  disabled.
- Keep the routing selection out of persistent configuration layers while
  preserving it across config refreshes and agent role changes.

## Testing

- Cover global flag parsing, app-server propagation, config-layer isolation,
  and preservation across config rebuilds and role changes.

GitOrigin-RevId: 05cdc61ffd7162d8e48fc1e166f4732113e5a816

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

@@ -445,7 +445,7 @@ async fn start_uninitialized(args: InProcessStartArgs) -> IoResult<InProcessClie
         ));
 
         let processor_outgoing = Arc::clone(&outgoing_message_sender);
-        let config_manager = ConfigManager::new(
+        let mut config_manager = ConfigManager::new(
             args.config.codex_home.to_path_buf(),
             args.cli_overrides,
             args.loader_overrides,
@@ -454,6 +454,7 @@ 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 {