Remove redundant Codex Apps manager flag (#29518)

## Why

Codex Apps server admission is already decided before
`McpConnectionManager` is constructed. `effective_mcp_servers` and
`effective_mcp_servers_from_configured` remove the server when the apps
feature or required authentication is unavailable, so storing the same
decision on the manager duplicates state that can drift from the
effective server map.

## What changed

- Remove `host_owned_codex_apps_enabled` from `McpConnectionManager` and
its constructor.
- Identify the host-owned Codex Apps server by its reserved server name
once it is present in the effective server map.
- Remove the now-unused flag calculations and constructor arguments from
production and test callsites.

codex-rs/codex-mcp/src/connection_manager.rs

@@ -109,7 +109,6 @@ pub struct McpConnectionManager {
     server_metadata: HashMap<String, McpServerMetadata>,
     required_servers: Vec<String>,
     tool_plugin_provenance: Arc<ToolPluginProvenance>,
-    host_owned_codex_apps_enabled: bool,
     prefix_mcp_tool_names: bool,
     elicitation_requests: ElicitationRequestManager,
     startup_cancellation_token: CancellationToken,
@@ -130,7 +129,6 @@ impl McpConnectionManager {
         runtime_context: McpRuntimeContext,
         codex_home: PathBuf,
         codex_apps_tools_cache_key: CodexAppsToolsCacheKey,
-        host_owned_codex_apps_enabled: bool,
         prefix_mcp_tool_names: bool,
         client_elicitation_capability: ElicitationCapability,
         supports_openai_form_elicitation: bool,
@@ -252,7 +250,6 @@ impl McpConnectionManager {
             server_metadata,
             required_servers,
             tool_plugin_provenance,
-            host_owned_codex_apps_enabled,
             prefix_mcp_tool_names,
             elicitation_requests: elicitation_requests.clone(),
             startup_cancellation_token: startup_cancellation_token.clone(),
@@ -338,7 +335,6 @@ impl McpConnectionManager {
             server_metadata: HashMap::new(),
             required_servers: Vec::new(),
             tool_plugin_provenance: Arc::new(ToolPluginProvenance::default()),
-            host_owned_codex_apps_enabled: false,
             prefix_mcp_tool_names,
             elicitation_requests: ElicitationRequestManager::new(
                 approval_policy.value(),
@@ -406,7 +402,7 @@ impl McpConnectionManager {
     }
 
     pub fn is_host_owned_codex_apps_server(&self, server_name: &str) -> bool {
-        self.host_owned_codex_apps_enabled && server_name == CODEX_APPS_MCP_SERVER_NAME
+        server_name == CODEX_APPS_MCP_SERVER_NAME
     }
 
     pub fn set_approval_policy(&self, approval_policy: &Constrained<AskForApproval>) {