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/tools/runtimes/apply_patch.rs

@@ -4,7 +4,6 @@
 //! decision to avoid re-prompting, builds the self-invocation command for
 //! `codex --codex-run-as-apply-patch`, and runs under the current
 //! `SandboxAttempt` with a minimal environment.
-use crate::CODEX_APPLY_PATCH_ARG1;
 use crate::exec::ExecToolCallOutput;
 use crate::sandboxing::CommandSpec;
 use crate::sandboxing::SandboxPermissions;
@@ -20,6 +19,7 @@ use crate::tools::sandboxing::ToolError;
 use crate::tools::sandboxing::ToolRuntime;
 use crate::tools::sandboxing::with_cached_approval;
 use codex_apply_patch::ApplyPatchAction;
+use codex_apply_patch::CODEX_CORE_APPLY_PATCH_ARG1;
 use codex_protocol::protocol::AskForApproval;
 use codex_protocol::protocol::FileChange;
 use codex_protocol::protocol::ReviewDecision;
@@ -57,7 +57,10 @@ impl ApplyPatchRuntime {
         let program = exe.to_string_lossy().to_string();
         Ok(CommandSpec {
             program,
-            args: vec![CODEX_APPLY_PATCH_ARG1.to_string(), req.action.patch.clone()],
+            args: vec![
+                CODEX_CORE_APPLY_PATCH_ARG1.to_string(),
+                req.action.patch.clone(),
+            ],
             cwd: req.action.cwd.clone(),
             expiration: req.timeout_ms.into(),
             // Run apply_patch with a minimal environment for determinism and to avoid leaks.