[apply-patch] Clean up apply-patch tool definitions (#2539)

## Summary
We've experienced a bit of drift in system prompting for `apply_patch`:
- As pointed out in #2030 , our prettier formatting started altering
prompt.md in a few ways
- We introduced a separate markdown file for apply_patch instructions in
#993, but currently duplicate them in the prompt.md file
- We added a first-class apply_patch tool in #2303, which has yet
another definition

This PR starts to consolidate our logic in a few ways:
- We now only use
`apply_patch_tool_instructions.md](https://github.com/openai/codex/compare/dh--apply-patch-tool-definition?expand=1#diff-d4fffee5f85cb1975d3f66143a379e6c329de40c83ed5bf03ffd3829df985bea)
for system instructions
- We no longer include apply_patch system instructions if the tool is
specified

I'm leaving the definition in openai_tools.rs as duplicated text for now
because we're going to be iterated on the first-class tool soon.

## Testing
- [x] Added integration tests to verify prompt stability
- [x] Tested locally with several different models (gpt-5, gpt-oss,
o4-mini)

codex-rs/core/src/client_common.rs

@@ -47,7 +47,17 @@ impl Prompt {
             .as_deref()
             .unwrap_or(BASE_INSTRUCTIONS);
         let mut sections: Vec<&str> = vec![base];
-        if model.needs_special_apply_patch_instructions {
+
+        // When there are no custom instructions, add apply_patch if either:
+        // - the model needs special instructions, or
+        // - there is no apply_patch tool present
+        let is_apply_patch_tool_present = self
+            .tools
+            .iter()
+            .any(|t| matches!(t, OpenAiTool::Function(f) if f.name == "apply_patch"));
+        if self.base_instructions_override.is_none()
+            && (model.needs_special_apply_patch_instructions || !is_apply_patch_tool_present)
+        {
             sections.push(APPLY_PATCH_TOOL_INSTRUCTIONS);
         }
         Cow::Owned(sections.join("\n"))