feat: make built-in MCPs first-class runtime servers (#21356)

## DISCLAIMER
This is experimental and no production service must rely on this

## Why

Built-in MCPs are product-owned runtime capabilities, but they were
previously flattened into the same config-backed stdio path as
user-configured servers. That made them depend on a hidden `codex
builtin-mcp` re-exec path, exposed them through config-oriented CLI
flows, and erased distinctions the runtime needs to preserve—most
notably whether an MCP call should count as external context for
memory-mode pollution.

## What changed

- Model product-owned built-ins separately from config-backed MCP
servers via `BuiltinMcpServer` and `EffectiveMcpServer`.
- Launch built-ins in process through a reusable async transport instead
of the hidden `builtin-mcp` stdio subcommand.
- Keep config-oriented CLI operations such as `codex mcp
list/get/login/logout` scoped to configured servers, while merging
built-ins only into the effective runtime server set.
- Retain server metadata after launch so parallel-tool support and
context classification come from the live server set; built-in
`memories` is now classified as local Codex state rather than external
context.

## Test plan

- `cargo test -p codex-mcp`
- `cargo test -p codex-core --test suite
builtin_memories_mcp_call_does_not_mark_thread_memory_mode_polluted_when_configured`

---------

Co-authored-by: Codex <noreply@openai.com>

codex-rs/core/src/tools/code_mode/mod.rs

@@ -4,7 +4,6 @@ mod response_adapter;
 mod wait_handler;
 pub(crate) mod wait_spec;
 
-use std::collections::HashSet;
 use std::sync::Arc;
 use std::time::Duration;
 
@@ -274,26 +273,9 @@ pub(super) async fn build_enabled_tools(
 )]
 async fn build_nested_router(exec: &ExecContext) -> ToolRouter {
     let nested_tools_config = exec.turn.tools_config.for_code_mode_nested_tools();
-    let listed_mcp_tools = exec
-        .session
-        .services
-        .mcp_connection_manager
-        .read()
-        .await
-        .list_all_tools()
-        .await;
-    let parallel_mcp_server_names = exec
-        .turn
-        .config
-        .mcp_servers
-        .get()
-        .iter()
-        .filter_map(|(server_name, server_config)| {
-            server_config
-                .supports_parallel_tool_calls
-                .then_some(server_name.clone())
-        })
-        .collect::<HashSet<_>>();
+    let mcp_connection_manager = exec.session.services.mcp_connection_manager.read().await;
+    let listed_mcp_tools = mcp_connection_manager.list_all_tools().await;
+    let parallel_mcp_server_names = mcp_connection_manager.parallel_tool_call_server_names();
 
     ToolRouter::from_config(
         &nested_tools_config,