codex-tools: extract code mode tool spec adapters (#16132)

## Why

The longer-term `codex-tools` migration is to move pure tool-definition
and tool-spec plumbing out of `codex-core` while leaving session- and
runtime-coupled orchestration behind.

The remaining code-mode adapter layer in
`core/src/tools/code_mode_description.rs` was a good next extraction
seam because it only transformed `ToolSpec` values for code mode and
already delegated the low-level description rendering to
`codex-code-mode`.

## What Changed

- added `codex-rs/tools/src/code_mode.rs` with
`augment_tool_spec_for_code_mode()` and
`tool_spec_to_code_mode_tool_definition()`
- added focused unit coverage in `codex-rs/tools/src/code_mode_tests.rs`
- rewired `core/src/tools/spec.rs` and `core/src/tools/code_mode/mod.rs`
to use the extracted adapters from `codex-tools`
- removed the old `core/src/tools/code_mode_description.rs` shim and its
test file from `codex-core`
- added the `codex-code-mode` dependency to `codex-tools`, updated
`Cargo.lock`, and refreshed the `codex-tools` README to reflect the
expanded boundary

## Test Plan

- `cargo test -p codex-tools`
- `CARGO_TARGET_DIR=/tmp/codex-core-code-mode-adapters cargo test -p
codex-core --lib tools::spec::`
- `CARGO_TARGET_DIR=/tmp/codex-core-code-mode-adapters cargo test -p
codex-core --lib tools::code_mode::`
- `just bazel-lock-update`
- `just bazel-lock-check`
- `just argument-comment-lint`

## References

- #15923
- #15928
- #15944
- #15953
- #16031
- #16047
- #16129

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

@@ -19,7 +19,6 @@ use crate::codex::Session;
 use crate::codex::TurnContext;
 use crate::function_tool::FunctionCallError;
 use crate::tools::ToolRouter;
-use crate::tools::code_mode_description::augment_tool_spec_for_code_mode;
 use crate::tools::context::FunctionToolOutput;
 use crate::tools::context::SharedTurnDiffTracker;
 use crate::tools::context::ToolPayload;
@@ -29,6 +28,7 @@ use crate::tools::router::ToolCallSource;
 use crate::tools::router::ToolRouterParams;
 use crate::unified_exec::resolve_max_tokens;
 use codex_features::Feature;
+use codex_tools::tool_spec_to_code_mode_tool_definition;
 use codex_utils_output_truncation::TruncationPolicy;
 use codex_utils_output_truncation::formatted_truncate_text_content_items_with_policy;
 use codex_utils_output_truncation::truncate_function_output_items_with_policy;
@@ -247,42 +247,13 @@ pub(super) async fn build_enabled_tools(
     let mut out = router
         .specs()
         .into_iter()
-        .map(|spec| augment_tool_spec_for_code_mode(spec, /*code_mode_enabled*/ true))
-        .filter_map(enabled_tool_from_spec)
+        .filter_map(|spec| tool_spec_to_code_mode_tool_definition(&spec))
         .collect::<Vec<_>>();
     out.sort_by(|left, right| left.name.cmp(&right.name));
     out.dedup_by(|left, right| left.name == right.name);
     out
 }
 
-fn enabled_tool_from_spec(spec: ToolSpec) -> Option<codex_code_mode::ToolDefinition> {
-    let tool_name = spec.name().to_string();
-    if !codex_code_mode::is_code_mode_nested_tool(&tool_name) {
-        return None;
-    }
-
-    match spec {
-        ToolSpec::Function(tool) => Some(codex_code_mode::ToolDefinition {
-            name: tool_name,
-            description: tool.description,
-            kind: codex_code_mode::CodeModeToolKind::Function,
-            input_schema: serde_json::to_value(&tool.parameters).ok(),
-            output_schema: tool.output_schema,
-        }),
-        ToolSpec::Freeform(tool) => Some(codex_code_mode::ToolDefinition {
-            name: tool_name,
-            description: tool.description,
-            kind: codex_code_mode::CodeModeToolKind::Freeform,
-            input_schema: None,
-            output_schema: None,
-        }),
-        ToolSpec::LocalShell {}
-        | ToolSpec::ImageGeneration { .. }
-        | ToolSpec::ToolSearch { .. }
-        | ToolSpec::WebSearch { .. } => None,
-    }
-}
-
 async fn build_nested_router(exec: &ExecContext) -> ToolRouter {
     let nested_tools_config = exec.turn.tools_config.for_code_mode_nested_tools();
     let mcp_tools = exec