[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/remote_legacy.rs

@@ -6,19 +6,9 @@ use serde::Deserialize;
 use std::time::Duration;
 use url::Url;
 
-const DEFAULT_REMOTE_MARKETPLACE_NAME: &str = "openai-curated";
-const REMOTE_PLUGIN_FETCH_TIMEOUT: Duration = Duration::from_secs(30);
 const REMOTE_FEATURED_PLUGIN_FETCH_TIMEOUT: Duration = Duration::from_secs(10);
 const REMOTE_PLUGIN_MUTATION_TIMEOUT: Duration = Duration::from_secs(30);
 
-#[derive(Debug, Clone, PartialEq, Eq, Deserialize)]
-pub struct RemotePluginStatusSummary {
-    pub name: String,
-    #[serde(default = "default_remote_marketplace_name")]
-    pub marketplace_name: String,
-    pub enabled: bool,
-}
-
 #[derive(Debug, Clone, PartialEq, Eq, Deserialize)]
 #[serde(rename_all = "camelCase")]
 struct RemotePluginMutationResponse {
@@ -83,32 +73,21 @@ pub enum RemotePluginMutationError {
 
 #[derive(Debug, thiserror::Error)]
 pub enum RemotePluginFetchError {
-    #[error("chatgpt authentication required to sync remote plugins")]
-    AuthRequired,
-
-    #[error(
-        "chatgpt authentication required to sync remote plugins; api key auth is not supported"
-    )]
-    UnsupportedAuthMode,
-
-    #[error("failed to read auth token for remote plugin sync: {0}")]
-    AuthToken(#[source] std::io::Error),
-
-    #[error("failed to send remote plugin sync request to {url}: {source}")]
+    #[error("failed to send remote featured plugin request to {url}: {source}")]
     Request {
         url: String,
         #[source]
         source: reqwest::Error,
     },
 
-    #[error("remote plugin sync request to {url} failed with status {status}: {body}")]
+    #[error("remote featured plugin request to {url} failed with status {status}: {body}")]
     UnexpectedStatus {
         url: String,
         status: reqwest::StatusCode,
         body: String,
     },
 
-    #[error("failed to parse remote plugin sync response from {url}: {source}")]
+    #[error("failed to parse remote featured plugin response from {url}: {source}")]
     Decode {
         url: String,
         #[source]
@@ -116,44 +95,6 @@ pub enum RemotePluginFetchError {
     },
 }
 
-pub async fn fetch_remote_plugin_status(
-    config: &RemotePluginServiceConfig,
-    auth: Option<&CodexAuth>,
-) -> Result<Vec<RemotePluginStatusSummary>, RemotePluginFetchError> {
-    let Some(auth) = auth else {
-        return Err(RemotePluginFetchError::AuthRequired);
-    };
-    if !auth.uses_codex_backend() {
-        return Err(RemotePluginFetchError::UnsupportedAuthMode);
-    }
-
-    let base_url = config.chatgpt_base_url.trim_end_matches('/');
-    let url = format!("{base_url}/plugins/list");
-    let client = build_reqwest_client();
-    let request = client
-        .get(&url)
-        .timeout(REMOTE_PLUGIN_FETCH_TIMEOUT)
-        .headers(codex_model_provider::auth_provider_from_auth(auth).to_auth_headers());
-
-    let response = request
-        .send()
-        .await
-        .map_err(|source| RemotePluginFetchError::Request {
-            url: url.clone(),
-            source,
-        })?;
-    let status = response.status();
-    let body = response.text().await.unwrap_or_default();
-    if !status.is_success() {
-        return Err(RemotePluginFetchError::UnexpectedStatus { url, status, body });
-    }
-
-    serde_json::from_str(&body).map_err(|source| RemotePluginFetchError::Decode {
-        url: url.clone(),
-        source,
-    })
-}
-
 pub async fn fetch_remote_featured_plugin_ids(
     config: &RemotePluginServiceConfig,
     auth: Option<&CodexAuth>,
@@ -224,10 +165,6 @@ fn ensure_codex_backend_auth(
     Ok(auth)
 }
 
-fn default_remote_marketplace_name() -> String {
-    DEFAULT_REMOTE_MARKETPLACE_NAME.to_string()
-}
-
 async fn post_remote_plugin_mutation(
     config: &RemotePluginServiceConfig,
     auth: Option<&CodexAuth>,