Move MCP tool naming mode into manager (#21576)

## Why

The `non_prefixed_mcp_tool_names` feature should be applied where MCP
tools become model-visible, not by remapping names later in core.
Keeping the decision in `McpConnectionManager` construction makes
`ToolInfo` the single shaped view that spec building, deferred tool
search, routing, and unavailable-tool placeholders can consume directly.

This also preserves the existing external behavior while the feature is
off, and keeps the feature-on behavior for code mode and hooks explicit
at the manager boundary.

## What Changed

- Add `McpToolNameMode` to `codex-mcp` and flow it through `McpConfig`
into `McpConnectionManager::new`.
- Normalize MCP `ToolInfo` names in the manager using either
legacy-prefixed namespaces or non-prefixed namespaces; the legacy path
adds `mcp__` without restoring the old trailing namespace suffix.
- Remove the core-side MCP name remapping path so specs, tool search,
session resolution, and unavailable-tool placeholder construction use
the manager-provided `ToolName` values directly.
- Keep code mode flattening on the `__` namespace separator.
- Preserve hook compatibility by giving non-prefixed MCP hook names
legacy `mcp__...` matcher aliases.
- Add/adjust integration and unit coverage for non-prefixed code-mode
behavior, hook matching with the feature on and off, and manager-level
legacy prefixing.

## Testing

- `cargo test -p codex-mcp --lib`
- `cargo test -p codex-core --lib tools::spec::tests -- --nocapture`
- `cargo test -p codex-core --lib mcp_tools -- --nocapture`
- `cargo test -p codex-core --lib mcp_tool_exposure -- --nocapture`
- `cargo test -p codex-core --test all mcp_tool -- --nocapture`
- `cargo test -p codex-core --test all search_tool -- --nocapture`
- `cargo test -p codex-core --test all hooks_mcp -- --nocapture`
- `cargo test -p codex-core --test all
code_mode_uses_non_prefixed_mcp_tool_names_when_feature_enabled --
--nocapture`
- `cargo test -p codex-tools`
- `cargo test -p codex-features`

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

@@ -33,7 +33,7 @@ use crate::server::EffectiveMcpServer;
 use crate::server::McpServerMetadata;
 use crate::tools::ToolInfo;
 use crate::tools::filter_tools;
-use crate::tools::normalize_tools_for_model;
+use crate::tools::normalize_tools_for_model_with_prefix;
 use crate::tools::tool_with_model_visible_input_schema;
 use anyhow::Context;
 use anyhow::Result;
@@ -73,6 +73,7 @@ pub struct McpConnectionManager {
     server_metadata: HashMap<String, McpServerMetadata>,
     tool_plugin_provenance: Arc<ToolPluginProvenance>,
     host_owned_codex_apps_enabled: bool,
+    prefix_mcp_tool_names: bool,
     elicitation_requests: ElicitationRequestManager,
     startup_cancellation_token: CancellationToken,
 }
@@ -81,19 +82,26 @@ impl McpConnectionManager {
     pub fn new_uninitialized(
         approval_policy: &Constrained<AskForApproval>,
         permission_profile: &Constrained<PermissionProfile>,
+        prefix_mcp_tool_names: bool,
     ) -> Self {
-        Self::new_uninitialized_with_permission_profile(approval_policy, permission_profile.get())
+        Self::new_uninitialized_with_permission_profile(
+            approval_policy,
+            permission_profile.get(),
+            prefix_mcp_tool_names,
+        )
     }
 
     pub fn new_uninitialized_with_permission_profile(
         approval_policy: &Constrained<AskForApproval>,
         permission_profile: &PermissionProfile,
+        prefix_mcp_tool_names: bool,
     ) -> Self {
         Self {
             clients: HashMap::new(),
             server_metadata: HashMap::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(),
                 permission_profile.clone(),
@@ -180,6 +188,7 @@ impl McpConnectionManager {
         codex_home: PathBuf,
         codex_apps_tools_cache_key: CodexAppsToolsCacheKey,
         host_owned_codex_apps_enabled: bool,
+        prefix_mcp_tool_names: bool,
         client_elicitation_capability: ElicitationCapability,
         tool_plugin_provenance: ToolPluginProvenance,
         auth: Option<&CodexAuth>,
@@ -292,6 +301,7 @@ impl McpConnectionManager {
             server_metadata,
             tool_plugin_provenance,
             host_owned_codex_apps_enabled,
+            prefix_mcp_tool_names,
             elicitation_requests: elicitation_requests.clone(),
             startup_cancellation_token: cancel_token.clone(),
         };
@@ -381,7 +391,7 @@ impl McpConnectionManager {
                     .map(|tool| self.with_server_metadata(tool)),
             );
         }
-        normalize_tools_for_model(tools)
+        normalize_tools_for_model_with_prefix(tools, self.prefix_mcp_tool_names)
     }
 
     /// Force-refresh codex apps tools by bypassing the in-process cache.
@@ -432,7 +442,10 @@ impl McpConnectionManager {
                 tool.tool = tool_with_model_visible_input_schema(&tool.tool);
                 self.with_server_metadata(tool)
             });
-        Ok(normalize_tools_for_model(tools))
+        Ok(normalize_tools_for_model_with_prefix(
+            tools,
+            self.prefix_mcp_tool_names,
+        ))
     }
 
     fn with_server_metadata(&self, mut tool: ToolInfo) -> ToolInfo {