[code mode] defer mcp tools from exec description (#17287)

## Summary
- hide deferred MCP/app nested tool descriptions from the `exec` prompt
in code mode
- add short guidance that omitted nested tools are still available
through `ALL_TOOLS`
- cover the code_mode_only path with an integration test that discovers
and calls a deferred app tool

## Motivation
`code_mode_only` exposes only top-level `exec`/`wait`, but the `exec`
description could still include a large nested-tool reference. This
keeps deferred nested tools callable while avoiding that prompt bloat.

## Tests
- `just fmt`
- `just fix -p codex-code-mode`
- `just fix -p codex-tools`
- `cargo test -p codex-code-mode
exec_description_mentions_deferred_nested_tools_when_available`
- `cargo test -p codex-tools
create_code_mode_tool_matches_expected_spec`
- `cargo test -p codex-core
code_mode_only_guides_all_tools_search_and_calls_deferred_app_tools`

codex-rs/tools/src/code_mode.rs

@@ -138,7 +138,8 @@ pub fn create_wait_tool() -> ToolSpec {
 pub fn create_code_mode_tool(
     enabled_tools: &[CodeModeToolDefinition],
     namespace_descriptions: &BTreeMap<String, codex_code_mode::ToolNamespaceDescription>,
-    code_mode_only_enabled: bool,
+    code_mode_only: bool,
+    deferred_tools_available: bool,
 ) -> ToolSpec {
     const CODE_MODE_FREEFORM_GRAMMAR: &str = r#"
 start: pragma_source | plain_source
@@ -155,7 +156,8 @@ SOURCE: /[\s\S]+/
         description: codex_code_mode::build_exec_tool_description(
             enabled_tools,
             namespace_descriptions,
-            code_mode_only_enabled,
+            code_mode_only,
+            deferred_tools_available,
         ),
         format: FreeformToolFormat {
             r#type: "grammar".to_string(),

codex-rs/tools/src/code_mode_tests.rs

@@ -197,14 +197,16 @@ fn create_code_mode_tool_matches_expected_spec() {
         create_code_mode_tool(
             &enabled_tools,
             &BTreeMap::new(),
-            /*code_mode_only_enabled*/ true,
+            /*code_mode_only*/ true,
+            /*deferred_tools_available*/ false,
         ),
         ToolSpec::Freeform(FreeformTool {
             name: codex_code_mode::PUBLIC_TOOL_NAME.to_string(),
             description: codex_code_mode::build_exec_tool_description(
                 &enabled_tools,
                 &BTreeMap::new(),
-                /*code_mode_only*/ true
+                /*code_mode_only*/ true,
+                /*deferred_tools_available*/ false
             ),
             format: FreeformToolFormat {
                 r#type: "grammar".to_string(),

codex-rs/tools/src/tool_registry_plan.rs

@@ -108,6 +108,10 @@ pub fn build_tool_registry_plan(
                 &enabled_tools,
                 &namespace_descriptions,
                 config.code_mode_only_enabled,
+                config.search_tool
+                    && params
+                        .deferred_mcp_tools
+                        .is_some_and(|tools| !tools.is_empty()),
             ),
             /*supports_parallel_tool_calls*/ false,
             config.code_mode_enabled,