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/tools/src/code_mode.rs

@@ -0,0 +1,60 @@
+use crate::ToolSpec;
+use codex_code_mode::CodeModeToolKind;
+use codex_code_mode::ToolDefinition as CodeModeToolDefinition;
+
+/// Augment tool descriptions with code-mode-specific exec samples.
+pub fn augment_tool_spec_for_code_mode(spec: ToolSpec) -> ToolSpec {
+    let Some(description) = code_mode_tool_definition_for_spec(&spec)
+        .map(codex_code_mode::augment_tool_definition)
+        .map(|definition| definition.description)
+    else {
+        return spec;
+    };
+
+    match spec {
+        ToolSpec::Function(mut tool) => {
+            tool.description = description;
+            ToolSpec::Function(tool)
+        }
+        ToolSpec::Freeform(mut tool) => {
+            tool.description = description;
+            ToolSpec::Freeform(tool)
+        }
+        other => other,
+    }
+}
+
+/// Convert a supported nested tool spec into the code-mode runtime shape,
+/// including the code-mode-specific description sample.
+pub fn tool_spec_to_code_mode_tool_definition(spec: &ToolSpec) -> Option<CodeModeToolDefinition> {
+    let definition = code_mode_tool_definition_for_spec(spec)?;
+    codex_code_mode::is_code_mode_nested_tool(&definition.name)
+        .then(|| codex_code_mode::augment_tool_definition(definition))
+}
+
+fn code_mode_tool_definition_for_spec(spec: &ToolSpec) -> Option<CodeModeToolDefinition> {
+    match spec {
+        ToolSpec::Function(tool) => Some(CodeModeToolDefinition {
+            name: tool.name.clone(),
+            description: tool.description.clone(),
+            kind: CodeModeToolKind::Function,
+            input_schema: serde_json::to_value(&tool.parameters).ok(),
+            output_schema: tool.output_schema.clone(),
+        }),
+        ToolSpec::Freeform(tool) => Some(CodeModeToolDefinition {
+            name: tool.name.clone(),
+            description: tool.description.clone(),
+            kind: CodeModeToolKind::Freeform,
+            input_schema: None,
+            output_schema: None,
+        }),
+        ToolSpec::LocalShell {}
+        | ToolSpec::ImageGeneration { .. }
+        | ToolSpec::ToolSearch { .. }
+        | ToolSpec::WebSearch { .. } => None,
+    }
+}
+
+#[cfg(test)]
+#[path = "code_mode_tests.rs"]
+mod tests;