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/main_tests.rs

@@ -46,7 +46,6 @@ fn app_server_accepts_process_scoped_code_mode_host() {
         "wss://example.test/code-mode",
         "--listen",
         "off",
-        "--psp",
     ])
     .expect("parse app-server args");
 
@@ -55,7 +54,6 @@ fn app_server_accepts_process_scoped_code_mode_host() {
         Some(Url::parse("wss://example.test/code-mode").expect("test endpoint should parse"))
     );
     assert_eq!(args.listen, AppServerTransport::Off);
-    assert!(args.psp);
     assert_eq!(args.config_overrides.raw_overrides, Vec::<String>::new());
 }