Simplify MCP tool handler plumbing (#21595)

## Why
The MCP tool path had accumulated a few core-owned special cases: a
dedicated payload variant, resolver plumbing, a legacy `AfterToolUse`
translation path, and a side channel for parallel-call metadata. That
made `ToolRegistry` and the spec builder know more about MCP than they
needed to.

This change moves MCP-specific execution details back onto `ToolInfo`
and `McpHandler` so `codex-core` can treat MCP calls like normal
function calls while still preserving MCP-specific dispatch and
telemetry behavior where it belongs.

## What changed
- removed `resolve_mcp_tool_info`, `ToolPayload::Mcp`, `ToolKind`, and
the remaining registry-side MCP resolver path
- stored MCP routing metadata directly on `McpHandler` and `ToolInfo`,
including `supports_parallel_tool_calls`
- deleted the legacy `AfterToolUse` consumer in `core`, which removes
the need for handler-specific `after_tool_use_payload` implementations
- switched tool-result telemetry to handler-provided tags and kept
MCP-specific dispatch payload construction inside the handler
- simplified tool spec planning/building by passing `ToolInfo` directly
and dropping the direct/deferred MCP wrapper structs and the
parallel-server side table

## Testing
- `cargo check -p codex-core -p codex-mcp -p codex-otel`
- `cargo test -p codex-core
mcp_parallel_support_uses_exact_payload_server`
- `cargo test -p codex-core
direct_mcp_tools_register_namespaced_handlers`
- `cargo test -p codex-core
search_tool_description_lists_each_mcp_source_once`
- `cargo test -p codex-mcp
list_all_tools_uses_startup_snapshot_while_client_is_pending`
- `just fix -p codex-core -p codex-mcp -p codex-otel`

codex-rs/core/src/session/mcp.rs

@@ -263,19 +263,6 @@ impl Session {
             .await
     }
 
-    #[expect(
-        clippy::await_holding_invalid_type,
-        reason = "MCP tool metadata reads through the session-owned manager guard"
-    )]
-    pub(crate) async fn resolve_mcp_tool_info(&self, tool_name: &ToolName) -> Option<ToolInfo> {
-        self.services
-            .mcp_connection_manager
-            .read()
-            .await
-            .resolve_tool_info(tool_name)
-            .await
-    }
-
     async fn refresh_mcp_servers_inner(
         &self,
         turn_context: &TurnContext,

codex-rs/core/src/session/mod.rs

@@ -64,7 +64,6 @@ use codex_login::auth_env_telemetry::collect_auth_env_telemetry;
 use codex_login::default_client::originator;
 use codex_mcp::McpConnectionManager;
 use codex_mcp::McpRuntimeEnvironment;
-use codex_mcp::ToolInfo;
 use codex_mcp::codex_apps_tools_cache_key;
 use codex_models_manager::manager::RefreshStrategy;
 use codex_models_manager::manager::SharedModelsManager;
@@ -75,7 +74,6 @@ use codex_otel::current_span_trace_id;
 use codex_otel::current_span_w3c_trace_context;
 use codex_otel::set_parent_from_w3c_trace_context;
 use codex_protocol::ThreadId;
-use codex_protocol::ToolName;
 use codex_protocol::account::PlanType as AccountPlanType;
 use codex_protocol::approvals::ElicitationRequestEvent;
 use codex_protocol::approvals::ExecPolicyAmendment;

codex-rs/core/src/session/tests.rs

@@ -543,7 +543,6 @@ fn test_tool_runtime(session: Arc<Session>, turn_context: Arc<TurnContext>) -> T
             mcp_tools: None,
             deferred_mcp_tools: None,
             unavailable_called_tools: Vec::new(),
-            parallel_mcp_server_names: HashSet::new(),
             discoverable_tools: None,
             extension_tool_bundles: Vec::new(),
             dynamic_tools: turn_context.dynamic_tools.as_slice(),
@@ -8641,7 +8640,6 @@ async fn fatal_tool_error_stops_turn_and_reports_error() {
             deferred_mcp_tools,
             mcp_tools: Some(tools),
             unavailable_called_tools: Vec::new(),
-            parallel_mcp_server_names: HashSet::new(),
             discoverable_tools: None,
             extension_tool_bundles: Vec::new(),
             dynamic_tools: turn_context.dynamic_tools.as_slice(),
@@ -8655,8 +8653,7 @@ async fn fatal_tool_error_stops_turn_and_reports_error() {
         input: "{}".to_string(),
     };
 
-    let call = ToolRouter::build_tool_call(session.as_ref(), item.clone())
-        .await
+    let call = ToolRouter::build_tool_call(item.clone())
         .expect("build tool call")
         .expect("tool call present");
     let tracker = Arc::new(tokio::sync::Mutex::new(TurnDiffTracker::new()));

codex-rs/core/src/session/turn.rs

@@ -1161,7 +1161,6 @@ pub(crate) async fn built_tools(
         .list_all_tools()
         .or_cancel(cancellation_token)
         .await?;
-    let parallel_mcp_server_names = mcp_connection_manager.parallel_tool_call_server_names();
     drop(mcp_connection_manager);
     let loaded_plugins = sess
         .services
@@ -1267,7 +1266,6 @@ pub(crate) async fn built_tools(
             mcp_tools,
             deferred_mcp_tools,
             unavailable_called_tools,
-            parallel_mcp_server_names,
             discoverable_tools,
             extension_tool_bundles: extension_tool_bundles(sess),
             dynamic_tools: turn_context.dynamic_tools.as_slice(),