[codex] Migrate apply_patch to executor filesystem (#17027)

- Migrate apply-patch verification and application internals to use the
async `ExecutorFileSystem` abstraction from `exec-server`.
- Convert apply-patch `cwd` handling to `AbsolutePathBuf` through the
verifier/parser/handler boundary.

Doesn't change how the tool itself works.

codex-rs/Cargo.lock

@@ -1543,11 +1543,14 @@ dependencies = [
  "anyhow",
  "assert_cmd",
  "assert_matches",
+ "codex-exec-server",
+ "codex-utils-absolute-path",
  "codex-utils-cargo-bin",
  "pretty_assertions",
  "similar",
  "tempfile",
  "thiserror 2.0.18",
+ "tokio",
  "tree-sitter",
  "tree-sitter-bash",
 ]
@@ -1558,9 +1561,11 @@ version = "0.0.0"
 dependencies = [
  "anyhow",
  "codex-apply-patch",
+ "codex-exec-server",
  "codex-linux-sandbox",
  "codex-sandboxing",
  "codex-shell-escalation",
+ "codex-utils-absolute-path",
  "codex-utils-home-dir",
  "dotenvy",
  "tempfile",