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/thread-manager-sample/src/main.rs

@@ -187,7 +187,6 @@ fn new_config(model: Option<String>, arg0_paths: Arg0DispatchPaths) -> anyhow::R
         config_layer_stack: ConfigLayerStack::default(),
         startup_warnings: Vec::new(),
         bypass_hook_trust: false,
-        psp: false,
         model,
         service_tier: None,
         review_model: None,