Extract MCP into codex-mcp crate (#15919)

- Split MCP runtime/server code out of `codex-core` into the new
`codex-mcp` crate. New/moved public structs/types include `McpConfig`,
`McpConnectionManager`, `ToolInfo`, `ToolPluginProvenance`,
`CodexAppsToolsCacheKey`, and the `McpManager` API
(`codex_mcp::mcp::McpManager` plus the `codex_core::mcp::McpManager`
wrapper/shim). New/moved functions include `with_codex_apps_mcp`,
`configured_mcp_servers`, `effective_mcp_servers`,
`collect_mcp_snapshot`, `collect_mcp_snapshot_from_manager`,
`qualified_mcp_tool_name_prefix`, and the MCP auth/skill-dependency
helpers. Why: this creates a focused MCP crate boundary and shrinks
`codex-core` without forcing every consumer to migrate in the same PR.

- Move MCP server config schema and persistence into `codex-config`.
New/moved structs/enums include `AppToolApproval`,
`McpServerToolConfig`, `McpServerConfig`, `RawMcpServerConfig`,
`McpServerTransportConfig`, `McpServerDisabledReason`, and
`codex_config::ConfigEditsBuilder`. New/moved functions include
`load_global_mcp_servers` and
`ConfigEditsBuilder::replace_mcp_servers`/`apply`. Why: MCP TOML
parsing/editing is config ownership, and this keeps config
validation/round-tripping (including per-tool approval overrides and
inline bearer-token rejection) in the config crate instead of
`codex-core`.

- Rewire `codex-core`, app-server, and plugin call sites onto the new
crates. Updated `Config::to_mcp_config(&self, plugins_manager)`,
`codex-rs/core/src/mcp.rs`, `codex-rs/core/src/connectors.rs`,
`codex-rs/core/src/codex.rs`,
`CodexMessageProcessor::list_mcp_server_status_task`, and
`utils/plugins/src/mcp_connector.rs` to build/pass the new MCP
config/runtime types. Why: plugin-provided MCP servers still merge with
user-configured servers, and runtime auth (`CodexAuth`) is threaded into
`with_codex_apps_mcp` / `collect_mcp_snapshot` explicitly so `McpConfig`
stays config-only.

codex-rs/core/src/codex_tests.rs

@@ -2654,11 +2654,9 @@ pub(crate) async fn make_session_and_context() -> (Session, TurnContext) {
 
     let skills_watcher = Arc::new(SkillsWatcher::noop());
     let services = SessionServices {
-        mcp_connection_manager: Arc::new(RwLock::new(
-            McpConnectionManager::new_mcp_connection_manager_for_tests(
-                &config.permissions.approval_policy,
-            ),
-        )),
+        mcp_connection_manager: Arc::new(RwLock::new(McpConnectionManager::new_uninitialized(
+            &config.permissions.approval_policy,
+        ))),
         mcp_startup_cancellation_token: Mutex::new(CancellationToken::new()),
         unified_exec_manager: UnifiedExecProcessManager::new(
             config.background_terminal_max_timeout,
@@ -3497,11 +3495,9 @@ pub(crate) async fn make_session_and_context_with_dynamic_tools_and_rx(
 
     let skills_watcher = Arc::new(SkillsWatcher::noop());
     let services = SessionServices {
-        mcp_connection_manager: Arc::new(RwLock::new(
-            McpConnectionManager::new_mcp_connection_manager_for_tests(
-                &config.permissions.approval_policy,
-            ),
-        )),
+        mcp_connection_manager: Arc::new(RwLock::new(McpConnectionManager::new_uninitialized(
+            &config.permissions.approval_policy,
+        ))),
         mcp_startup_cancellation_token: Mutex::new(CancellationToken::new()),
         unified_exec_manager: UnifiedExecProcessManager::new(
             config.background_terminal_max_timeout,