core: use codex-mcp APIs directly (#16510)

## Why

`codex-mcp` already owns the shared MCP API surface, including `auth`,
`McpConfig`, `CODEX_APPS_MCP_SERVER_NAME`, and tool-name helpers in
[`codex-rs/codex-mcp/src/mcp/mod.rs`](https://github.com/openai/codex/blob/f61e85dbfb5373cde6827d232ac8ea447c237e81/codex-rs/codex-mcp/src/mcp/mod.rs#L1-L35).
Re-exporting that surface from `codex_core::mcp` gives downstream crates
two import paths for the same API and hides the real crate dependency.

This PR keeps `codex_core::mcp` focused on the local `McpManager`
wrapper in
[`codex-rs/core/src/mcp.rs`](https://github.com/openai/codex/blob/f61e85dbfb5373cde6827d232ac8ea447c237e81/codex-rs/core/src/mcp.rs#L13-L40)
and makes consumers import shared MCP APIs from `codex_mcp` directly.

## What

- Remove the `codex_mcp::mcp` re-export surface from `core/src/mcp.rs`.
- Update `codex-core` internals plus `codex-app-server`, `codex-cli`,
and `codex-tui` test code to import MCP APIs from `codex_mcp::mcp`
directly.
- Add explicit `codex-mcp` dependencies where those crates now use that
API surface, and refresh `Cargo.lock`.

## Verification

- `just bazel-lock-check`
- `cargo test -p codex-core -p codex-cli -p codex-tui`
  - `codex-cli` passed.
- `codex-core` still fails five unrelated config tests in
`core/src/config/config_tests.rs` (`approvals_reviewer_*` and
`smart_approvals_alias_*`).
- A broader `cargo test -p codex-core -p codex-app-server -p codex-cli
-p codex-tui` run previously hung in `codex-app-server` test
`in_process_start_uses_requested_session_source_for_thread_start`.

codex-rs/app-server/src/codex_message_processor.rs

@@ -218,10 +218,6 @@ use codex_core::find_archived_thread_path_by_id_str;
 use codex_core::find_thread_name_by_id;
 use codex_core::find_thread_names_by_ids;
 use codex_core::find_thread_path_by_id_str;
-use codex_core::mcp::auth::discover_supported_scopes;
-use codex_core::mcp::auth::resolve_oauth_scopes;
-use codex_core::mcp::collect_mcp_snapshot;
-use codex_core::mcp::group_tools_by_server;
 use codex_core::models_manager::collaboration_mode_presets::CollaborationModesConfig;
 use codex_core::parse_cursor;
 use codex_core::plugins::MarketplaceError;
@@ -254,6 +250,10 @@ use codex_login::auth::login_with_chatgpt_auth_tokens;
 use codex_login::complete_device_code_login;
 use codex_login::request_device_code;
 use codex_login::run_login_server;
+use codex_mcp::mcp::auth::discover_supported_scopes;
+use codex_mcp::mcp::auth::resolve_oauth_scopes;
+use codex_mcp::mcp::collect_mcp_snapshot;
+use codex_mcp::mcp::group_tools_by_server;
 use codex_protocol::ThreadId;
 use codex_protocol::config_types::CollaborationMode;
 use codex_protocol::config_types::ForcedLoginMethod;
@@ -5053,7 +5053,7 @@ impl CodexMessageProcessor {
         request_id: ConnectionRequestId,
         params: ListMcpServerStatusParams,
         config: Config,
-        mcp_config: codex_core::mcp::McpConfig,
+        mcp_config: codex_mcp::mcp::McpConfig,
         auth: Option<CodexAuth>,
     ) {
         let snapshot = collect_mcp_snapshot(