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/core/src/session/mcp.rs

@@ -353,6 +353,7 @@ impl Session {
             config.codex_home.to_path_buf(),
             codex_apps_tools_cache_key(auth.as_ref()),
             host_owned_codex_apps_enabled,
+            mcp_config.prefix_mcp_tool_names,
             mcp_config.client_elicitation_capability,
             tool_plugin_provenance,
             auth.as_ref(),

codex-rs/core/src/session/session.rs

@@ -978,6 +978,7 @@ impl Session {
                     McpConnectionManager::new_uninitialized_with_permission_profile(
                         &config.permissions.approval_policy,
                         config.permissions.permission_profile(),
+                        config.prefix_mcp_tool_names(),
                     ),
                 )),
                 mcp_startup_cancellation_token: Mutex::new(CancellationToken::new()),
@@ -1156,6 +1157,7 @@ impl Session {
                 config.codex_home.to_path_buf(),
                 codex_apps_tools_cache_key(auth),
                 host_owned_codex_apps_enabled,
+                config.prefix_mcp_tool_names(),
                 client_elicitation_capability,
                 tool_plugin_provenance,
                 auth,

codex-rs/core/src/session/tests.rs

@@ -4519,6 +4519,7 @@ pub(crate) async fn make_session_and_context() -> (Session, TurnContext) {
             McpConnectionManager::new_uninitialized_with_permission_profile(
                 &config.permissions.approval_policy,
                 config.permissions.permission_profile(),
+                config.prefix_mcp_tool_names(),
             ),
         )),
         mcp_startup_cancellation_token: Mutex::new(CancellationToken::new()),
@@ -6348,6 +6349,7 @@ where
             McpConnectionManager::new_uninitialized_with_permission_profile(
                 &config.permissions.approval_policy,
                 config.permissions.permission_profile(),
+                config.prefix_mcp_tool_names(),
             ),
         )),
         mcp_startup_cancellation_token: Mutex::new(CancellationToken::new()),