[codex] Remove legacy remote plugin startup sync (#25936)

## Summary

- Remove the legacy startup remote plugin sync path that called
`/plugins/list` and reconciled curated plugin cache/config.
- Remove the `sync_plugins_from_remote` API, its result/error types,
startup marker task, and tests that expected the legacy request.
- Keep the current remote installed bundle sync and remote catalog flows
(`/ps/plugins/installed` and `/ps/plugins/list`) intact.

## Validation

- `just fmt`
- `git diff --check`
- `env HOME=/private/tmp/codex-xin-build-home
USERPROFILE=/private/tmp/codex-xin-build-home just test -p
codex-core-plugins`
- Searched for legacy `/plugins/list` sync references; remaining matches
are `/ps/plugins/list` catalog tests/code.

## Notes

- `just test -p codex-app-server plugin_list` is currently blocked
before running filtered tests by an unrelated compile error in
`app-server/tests/suite/v2/image_generation.rs`:
`app_test_support::McpProcess` is not exported.

codex-rs/core-plugins/src/test_support.rs

@@ -88,10 +88,6 @@ pub(crate) fn write_openai_curated_marketplace(root: &Path, plugin_names: &[&str
     }
 }
 
-pub(crate) fn write_curated_plugin_sha(codex_home: &Path) {
-    write_curated_plugin_sha_with(codex_home, TEST_CURATED_PLUGIN_SHA);
-}
-
 pub(crate) fn write_curated_plugin_sha_with(codex_home: &Path, sha: &str) {
     write_file(&codex_home.join(".tmp/plugins.sha"), &format!("{sha}\n"));
 }