[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/prompt.md

@@ -270,67 +270,6 @@ When using the shell, you must adhere to the following guidelines:
 - When searching for text or files, prefer using `rg` or `rg --files` respectively because `rg` is much faster than alternatives like `grep`. (If the `rg` command is not found, then use alternatives.)
 - Read files in chunks with a max chunk size of 250 lines. Do not use python scripts to attempt to output larger chunks of a file. Command line output will be truncated after 10 kilobytes or 256 lines of output, regardless of the command used.
 
-## `apply_patch`
-
-Your patch language is a stripped‑down, file‑oriented diff format designed to be easy to parse and safe to apply. You can think of it as a high‑level envelope:
-
-**_ Begin Patch
-[ one or more file sections ]
-_** End Patch
-
-Within that envelope, you get a sequence of file operations.
-You MUST include a header to specify the action you are taking.
-Each operation starts with one of three headers:
-
-**_ Add File: <path> - create a new file. Every following line is a + line (the initial contents).
-_** Delete File: <path> - remove an existing file. Nothing follows.
-\*\*\* Update File: <path> - patch an existing file in place (optionally with a rename).
-
-May be immediately followed by \*\*\* Move to: <new path> if you want to rename the file.
-Then one or more “hunks”, each introduced by @@ (optionally followed by a hunk header).
-Within a hunk each line starts with:
-
-- for inserted text,
-
-* for removed text, or
-  space ( ) for context.
-  At the end of a truncated hunk you can emit \*\*\* End of File.
-
-Patch := Begin { FileOp } End
-Begin := "**_ Begin Patch" NEWLINE
-End := "_** End Patch" NEWLINE
-FileOp := AddFile | DeleteFile | UpdateFile
-AddFile := "**_ Add File: " path NEWLINE { "+" line NEWLINE }
-DeleteFile := "_** Delete File: " path NEWLINE
-UpdateFile := "**_ Update File: " path NEWLINE [ MoveTo ] { Hunk }
-MoveTo := "_** Move to: " newPath NEWLINE
-Hunk := "@@" [ header ] NEWLINE { HunkLine } [ "*** End of File" NEWLINE ]
-HunkLine := (" " | "-" | "+") text NEWLINE
-
-A full patch can combine several operations:
-
-**_ Begin Patch
-_** Add File: hello.txt
-+Hello world
-**_ Update File: src/app.py
-_** Move to: src/main.py
-@@ def greet():
--print("Hi")
-+print("Hello, world!")
-**_ Delete File: obsolete.txt
-_** End Patch
-
-It is important to remember:
-
-- You must include a header with your intended action (Add/Delete/Update)
-- You must prefix new lines with `+` even when creating a new file
-
-You can invoke apply_patch like:
-
-```
-shell {"command":["apply_patch","*** Begin Patch\n*** Add File: hello.txt\n+Hello, world!\n*** End Patch\n"]}
-```
-
 ## `update_plan`
 
 A tool named `update_plan` is available to you. You can use it to keep an up‑to‑date, step‑by‑step plan for the task.