Centralize Codex Apps client handling (#29528)

## Why

Codex Apps-specific behavior is currently distributed across cache
helpers, startup, tool conversion, and model-visible annotation. Each
layer independently checks the reserved server name, which obscures the
boundary between trusted host-owned connector metadata and regular MCP
server data.

Classifying the server once when `AsyncManagedClient` is created gives
the client a single source of truth and makes the two processing paths
explicit.

## What changed

- Record whether an `AsyncManagedClient` represents the Codex Apps
server at construction time.
- Route startup cache loading, cache persistence, and cache telemetry
through the Codex Apps branch.
- Split uncached tool conversion between Codex Apps normalization and
regular MCP metadata sanitization.
- Split model-visible schema and plugin provenance handling along the
same boundary.
- Remove redundant server-name guards from helpers that are now called
only from the Codex Apps branch.

## Verification

- Preserve behavioral coverage that verifies Codex Apps connector
metadata and the complete converted `ToolInfo` shape.

## Stack

Depends on #29518.

codex-rs/codex-mcp/src/codex_apps.rs

@@ -66,15 +66,7 @@ pub(crate) enum CachedCodexAppsToolsLoad {
     Invalid,
 }
 
-pub(crate) fn normalize_codex_apps_tool_title(
-    server_name: &str,
-    connector_name: Option<&str>,
-    value: &str,
-) -> String {
-    if server_name != CODEX_APPS_MCP_SERVER_NAME {
-        return value.to_string();
-    }
-
+pub(crate) fn normalize_codex_apps_tool_title(connector_name: Option<&str>, value: &str) -> String {
     let Some(connector_name) = connector_name
         .map(str::trim)
         .filter(|name| !name.is_empty())
@@ -93,15 +85,10 @@ pub(crate) fn normalize_codex_apps_tool_title(
 }
 
 pub(crate) fn normalize_codex_apps_callable_name(
-    server_name: &str,
     tool_name: &str,
     connector_id: Option<&str>,
     connector_name: Option<&str>,
 ) -> String {
-    if server_name != CODEX_APPS_MCP_SERVER_NAME {
-        return tool_name.to_string();
-    }
-
     let tool_name = sanitize_name(tool_name);
 
     if let Some(connector_name) = connector_name
@@ -131,9 +118,7 @@ pub(crate) fn normalize_codex_apps_callable_namespace(
     server_name: &str,
     connector_name: Option<&str>,
 ) -> String {
-    if server_name == CODEX_APPS_MCP_SERVER_NAME
-        && let Some(connector_name) = connector_name
-    {
+    if let Some(connector_name) = connector_name {
         format!("{}__{}", server_name, sanitize_name(connector_name))
     } else {
         server_name.to_string()
@@ -165,13 +150,8 @@ pub(crate) fn write_cached_codex_apps_tools_if_needed(
 }
 
 pub(crate) fn load_startup_cached_codex_apps_tools_snapshot(
-    server_name: &str,
     cache_context: Option<&CodexAppsToolsCacheContext>,
 ) -> Option<Vec<ToolInfo>> {
-    if server_name != CODEX_APPS_MCP_SERVER_NAME {
-        return None;
-    }
-
     let cache_context = cache_context?;
 
     match load_cached_codex_apps_tools(cache_context) {
@@ -181,13 +161,8 @@ pub(crate) fn load_startup_cached_codex_apps_tools_snapshot(
 }
 
 pub(crate) fn load_startup_cached_codex_apps_server_info(
-    server_name: &str,
     cache_context: Option<&CodexAppsToolsCacheContext>,
 ) -> Option<McpServerInfo> {
-    if server_name != CODEX_APPS_MCP_SERVER_NAME {
-        return None;
-    }
-
     load_cached_codex_apps_server_info(cache_context?)
 }