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/core/src/apply_patch.rs

@@ -9,8 +9,6 @@ use codex_apply_patch::ApplyPatchFileChange;
 use std::collections::HashMap;
 use std::path::PathBuf;
 
-pub const CODEX_APPLY_PATCH_ARG1: &str = "--codex-run-as-apply-patch";
-
 pub(crate) enum InternalApplyPatchInvocation {
     /// The `apply_patch` call was handled programmatically, without any sort
     /// of sandbox, because the user explicitly approved it. This is the
@@ -20,7 +18,8 @@ pub(crate) enum InternalApplyPatchInvocation {
     /// The `apply_patch` call was approved, either automatically because it
     /// appears that it should be allowed based on the user's sandbox policy
     /// *or* because the user explicitly approved it. In either case, we use
-    /// exec with [`CODEX_APPLY_PATCH_ARG1`] to realize the `apply_patch` call,
+    /// exec with [`codex_apply_patch::CODEX_CORE_APPLY_PATCH_ARG1`] to realize
+    /// the `apply_patch` call,
     /// but [`ApplyPatchExec::auto_approved`] is used to determine the sandbox
     /// used with the `exec()`.
     DelegateToExec(ApplyPatchExec),