[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/core/src/apply_patch_tests.rs

@@ -1,4 +1,5 @@
 use super::*;
+use core_test_support::PathBufExt;
 use pretty_assertions::assert_eq;
 
 use tempfile::tempdir;
@@ -6,14 +7,14 @@ use tempfile::tempdir;
 #[test]
 fn convert_apply_patch_maps_add_variant() {
     let tmp = tempdir().expect("tmp");
-    let p = tmp.path().join("a.txt");
+    let p = tmp.path().join("a.txt").abs();
     // Create an action with a single Add change
     let action = ApplyPatchAction::new_add_for_test(&p, "hello".to_string());
 
     let got = convert_apply_patch_to_protocol(&action);
 
     assert_eq!(
-        got.get(&p),
+        got.get(p.as_path()),
         Some(&FileChange::Add {
             content: "hello".to_string()
         })