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/codex_apps.rs

@@ -20,7 +20,7 @@ use serde::Serialize;
 use sha1::Digest;
 use sha1::Sha1;
 
-pub(crate) const CODEX_APPS_TOOLS_CACHE_SCHEMA_VERSION: u8 = 2;
+pub(crate) const CODEX_APPS_TOOLS_CACHE_SCHEMA_VERSION: u8 = 3;
 
 #[derive(Debug, Clone, PartialEq, Eq, Serialize, Deserialize)]
 pub struct CodexAppsToolsCacheKey {
@@ -127,9 +127,9 @@ pub(crate) fn normalize_codex_apps_callable_namespace(
     if server_name == CODEX_APPS_MCP_SERVER_NAME
         && let Some(connector_name) = connector_name
     {
-        format!("mcp__{}__{}", server_name, sanitize_name(connector_name))
+        format!("{}__{}", server_name, sanitize_name(connector_name))
     } else {
-        format!("mcp__{server_name}__")
+        server_name.to_string()
     }
 }