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/features/src/lib.rs

@@ -136,6 +136,8 @@ pub enum Feature {
     ToolSearch,
     /// Always defer MCP tools behind tool_search instead of exposing small sets directly.
     ToolSearchAlwaysDeferMcpTools,
+    /// Expose MCP model-visible namespaces without the legacy `mcp__` prefix.
+    NonPrefixedMcpToolNames,
     /// Enable discoverable tool suggestions for apps.
     ToolSuggest,
     /// Enable plugins.
@@ -961,6 +963,12 @@ pub const FEATURES: &[FeatureSpec] = &[
         stage: Stage::UnderDevelopment,
         default_enabled: false,
     },
+    FeatureSpec {
+        id: Feature::NonPrefixedMcpToolNames,
+        key: "non_prefixed_mcp_tool_names",
+        stage: Stage::UnderDevelopment,
+        default_enabled: false,
+    },
     FeatureSpec {
         id: Feature::UnavailableDummyTools,
         key: "unavailable_dummy_tools",