fix: codex-arg0 no longer depends on codex-core (#12434)

## Why

`codex-rs/arg0` only needed two things from `codex-core`:

- the `find_codex_home()` wrapper
- the special argv flag used for the internal `apply_patch`
self-invocation path

That made `codex-arg0` depend on `codex-core` for a very small surface
area. This change removes that dependency edge and moves the shared
`apply_patch` invocation flag to a more natural boundary
(`codex-apply-patch`) while keeping the contract explicitly documented.

## What Changed

- Moved the internal `apply_patch` argv[1] flag constant out of
`codex-core` and into `codex-apply-patch`.
- Renamed the constant to `CODEX_CORE_APPLY_PATCH_ARG1` and documented
that it is part of the Codex core process-invocation contract (even
though it now lives in `codex-apply-patch`).
- Updated `arg0`, the core apply-patch runtime, and the `codex-exec`
apply-patch test to import the constant from `codex-apply-patch`.
- Updated `codex-rs/arg0` to call
`codex_utils_home_dir::find_codex_home()` directly instead of
`codex_core::config::find_codex_home()`.
- Removed the `codex-core` dependency from `codex-rs/arg0` and added the
needed direct dependency on `codex-utils-home-dir`.
- Added `codex-apply-patch` as a dev-dependency for `codex-rs/exec`
tests (the apply-patch test now imports the moved constant directly).

## Verification

- `cargo test -p codex-apply-patch`
- `cargo test -p codex-arg0`
- `cargo test -p codex-core --lib apply_patch`
- `cargo test -p codex-exec
test_standalone_exec_cli_can_use_apply_patch`
- `cargo shear`

codex-rs/apply-patch/src/lib.rs

@@ -25,6 +25,15 @@ use crate::invocation::ExtractHeredocError;
 /// Detailed instructions for gpt-4.1 on how to use the `apply_patch` tool.
 pub const APPLY_PATCH_TOOL_INSTRUCTIONS: &str = include_str!("../apply_patch_tool_instructions.md");
 
+/// Special argv[1] flag used when the Codex executable self-invokes to run the
+/// internal `apply_patch` path.
+///
+/// Although this constant lives in `codex-apply-patch` (to avoid forcing
+/// `codex-arg0` to depend on `codex-core`), it is part of the "codex core"
+/// process-invocation contract between the apply-patch runtime and the arg0
+/// dispatcher.
+pub const CODEX_CORE_APPLY_PATCH_ARG1: &str = "--codex-run-as-apply-patch";
+
 #[derive(Debug, Error, PartialEq)]
 pub enum ApplyPatchError {
     #[error(transparent)]