Cleanup code_mode tool descriptions (#14480)

Move to separate files and clarify a bit.

codex-rs/core/src/project_doc.rs

@@ -25,7 +25,6 @@ use crate::plugins::PluginCapabilitySummary;
 use crate::plugins::render_plugins_section;
 use crate::skills::SkillMetadata;
 use crate::skills::render_skills_section;
-use crate::tools::code_mode;
 use codex_app_server_protocol::ConfigLayerSource;
 use dunce::canonicalize as normalize_path;
 use std::path::PathBuf;
@@ -120,13 +119,6 @@ pub(crate) async fn get_user_instructions(
         output.push_str(&plugin_section);
     }
 
-    if let Some(code_mode_section) = code_mode::instructions(config) {
-        if !output.is_empty() {
-            output.push_str("\n\n");
-        }
-        output.push_str(&code_mode_section);
-    }
-
     let skills_section = skills.and_then(render_skills_section);
     if let Some(skills_section) = skills_section {
         if !output.is_empty() {